{"id":9200,"date":"2022-01-03T01:59:37","date_gmt":"2022-01-02T20:29:37","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9200"},"modified":"2022-01-03T02:13:01","modified_gmt":"2022-01-02T20:43:01","slug":"prove-that-sin2-theta-cos2-theta-1","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/","title":{"rendered":"Prove that \\(sin^2 \\theta\\) + \\(cos^2 \\theta\\) = 1."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>In right angled triangle ABC,<img decoding=\"async\" loading=\"lazy\" class=\"size-medium wp-image-9201 alignright\" src=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/01\/triangle-e1641154796978-300x236.png?resize=300%2C236&#038;ssl=1\" alt=\"\" width=\"300\" height=\"236\" srcset=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/01\/triangle-e1641154796978.png?resize=300%2C236&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/01\/triangle-e1641154796978.png?resize=768%2C604&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/01\/triangle-e1641154796978.png?w=834&amp;ssl=1 834w\" sizes=\"(max-width: 300px) 100vw, 300px\" data-recalc-dims=\"1\" \/><\/p>\n<p>\\(sin \\theta\\) = \\(BC\\over AC\\)&nbsp; \\(\\implies\\)&nbsp; &nbsp;\\(sin^2 \\theta\\) = \\(BC^2\\over AC^2\\)<\/p>\n<p>\\(cos \\theta\\) = \\(AB\\over AC\\)&nbsp; \\(\\implies\\)&nbsp; &nbsp;\\(cos^2 \\theta\\) = \\(AB^2\\over AC^2\\)<\/p>\n<p>On adding,<\/p>\n<p>\\(sin^2 \\theta\\) + \\(cos^2 \\theta\\) = \\(BC^2\\over AC^2\\) + \\(AB^2\\over AC^2\\)<\/p>\n<p>\\(sin^2 \\theta\\) + \\(cos^2 \\theta\\) = \\(BC^2 + AB^2\\over AC^2\\) = \\(AC^2\\over AC^2\\) = 1<\/p>\n<p>[ By Pythagoras theorem,&nbsp; \\(AC^2\\) = \\(BC^2 + AB^2\\) ]<\/p>\n<p>\\(\\implies\\) \\(sin^2 \\theta\\) + \\(cos^2 \\theta\\) = 1<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : In right angled triangle ABC, \\(sin \\theta\\) = \\(BC\\over AC\\)&nbsp; \\(\\implies\\)&nbsp; &nbsp;\\(sin^2 \\theta\\) = \\(BC^2\\over AC^2\\) \\(cos \\theta\\) = \\(AB\\over AC\\)&nbsp; \\(\\implies\\)&nbsp; &nbsp;\\(cos^2 \\theta\\) = \\(AB^2\\over AC^2\\) On adding, \\(sin^2 \\theta\\) + \\(cos^2 \\theta\\) = \\(BC^2\\over AC^2\\) + \\(AB^2\\over AC^2\\) \\(sin^2 \\theta\\) + \\(cos^2 \\theta\\) = \\(BC^2 + AB^2\\over AC^2\\) = \\(AC^2\\over AC^2\\) &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/\"> <span class=\"screen-reader-text\">Prove that \\(sin^2 \\theta\\) + \\(cos^2 \\theta\\) = 1.<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,60],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Prove that \\(sin^2 \\theta\\) + \\(cos^2 \\theta\\) = 1. - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Prove that \\(sin^2 \\theta\\) + \\(cos^2 \\theta\\) = 1. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : In right angled triangle ABC, (sin theta) = (BCover AC)&nbsp; (implies)&nbsp; &nbsp;(sin^2 theta) = (BC^2over AC^2) (cos theta) = (ABover AC)&nbsp; (implies)&nbsp; &nbsp;(cos^2 theta) = (AB^2over AC^2) On adding, (sin^2 theta) + (cos^2 theta) = (BC^2over AC^2) + (AB^2over AC^2) (sin^2 theta) + (cos^2 theta) = (BC^2 + AB^2over AC^2) = (AC^2over AC^2) &hellip; Prove that (sin^2 theta) + (cos^2 theta) = 1. Read More &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2022-01-02T20:29:37+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-01-02T20:43:01+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathemerize.com\/wp-content\/uploads\/2022\/01\/triangle-e1641154796978-300x236.png\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Prove that \\\\(sin^2 \\\\theta\\\\) + \\\\(cos^2 \\\\theta\\\\) = 1.\",\"datePublished\":\"2022-01-02T20:29:37+00:00\",\"dateModified\":\"2022-01-02T20:43:01+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/\"},\"wordCount\":75,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Maths Questions\",\"Trigonometry Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/\",\"url\":\"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/\",\"name\":\"Prove that \\\\(sin^2 \\\\theta\\\\) + \\\\(cos^2 \\\\theta\\\\) = 1. - Mathemerize\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2022-01-02T20:29:37+00:00\",\"dateModified\":\"2022-01-02T20:43:01+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Prove that \\\\(sin^2 \\\\theta\\\\) + \\\\(cos^2 \\\\theta\\\\) = 1.\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Prove that \\(sin^2 \\theta\\) + \\(cos^2 \\theta\\) = 1. - Mathemerize","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/","og_locale":"en_US","og_type":"article","og_title":"Prove that \\(sin^2 \\theta\\) + \\(cos^2 \\theta\\) = 1. - Mathemerize","og_description":"Solution : In right angled triangle ABC, (sin theta) = (BCover AC)&nbsp; (implies)&nbsp; &nbsp;(sin^2 theta) = (BC^2over AC^2) (cos theta) = (ABover AC)&nbsp; (implies)&nbsp; &nbsp;(cos^2 theta) = (AB^2over AC^2) On adding, (sin^2 theta) + (cos^2 theta) = (BC^2over AC^2) + (AB^2over AC^2) (sin^2 theta) + (cos^2 theta) = (BC^2 + AB^2over AC^2) = (AC^2over AC^2) &hellip; Prove that (sin^2 theta) + (cos^2 theta) = 1. Read More &raquo;","og_url":"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/","og_site_name":"Mathemerize","article_published_time":"2022-01-02T20:29:37+00:00","article_modified_time":"2022-01-02T20:43:01+00:00","og_image":[{"url":"https:\/\/mathemerize.com\/wp-content\/uploads\/2022\/01\/triangle-e1641154796978-300x236.png"}],"author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"Prove that \\(sin^2 \\theta\\) + \\(cos^2 \\theta\\) = 1.","datePublished":"2022-01-02T20:29:37+00:00","dateModified":"2022-01-02T20:43:01+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/"},"wordCount":75,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Maths Questions","Trigonometry Questions"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/","url":"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/","name":"Prove that \\(sin^2 \\theta\\) + \\(cos^2 \\theta\\) = 1. - Mathemerize","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2022-01-02T20:29:37+00:00","dateModified":"2022-01-02T20:43:01+00:00","breadcrumb":{"@id":"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/prove-that-sin2-theta-cos2-theta-1\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"Prove that \\(sin^2 \\theta\\) + \\(cos^2 \\theta\\) = 1."}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/9200"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=9200"}],"version-history":[{"count":2,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/9200\/revisions"}],"predecessor-version":[{"id":9208,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/9200\/revisions\/9208"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=9200"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=9200"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=9200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}