{"id":11705,"date":"2022-08-14T23:49:02","date_gmt":"2022-08-14T18:19:02","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11705"},"modified":"2022-08-14T23:49:09","modified_gmt":"2022-08-14T18:19:09","slug":"if-tan-a-b-sqrt3-and-tan-a-b-1over-sqrt3-0-a-b-le-90-a-ge-b-find-a-and-b","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-tan-a-b-sqrt3-and-tan-a-b-1over-sqrt3-0-a-b-le-90-a-ge-b-find-a-and-b\/","title":{"rendered":"If tan (A + B) = \\(\\sqrt{3}\\) and tan (A &#8211; B) = \\(1\\over \\sqrt{3}\\) ; 0 < A + B \\(\\le\\) 90 ; A \\(\\ge\\) B, find A and B."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>We have, tan (A + B) = \\(\\sqrt{3}\\)<\/p>\n<p>\\(\\implies\\)\u00a0 tan (A + B) = tan 60 \\(\\implies\\)\u00a0 A + B = 60\u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;&#8230;&#8230;(1)<\/p>\n<p>Also, tan (A &#8211; B) = \\(1\\over \\sqrt{3}\\)<\/p>\n<p>\\(\\implies\\)\u00a0 tan(A &#8211; B) = tan 30 \\(\\implies\\)\u00a0 A &#8211; B = 30\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 &#8230;&#8230;&#8230;&#8230;(2)<\/p>\n<p>Solving (1) and (2), we get<\/p>\n<p><strong>A = 45 and B = 15<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : We have, tan (A + B) = \\(\\sqrt{3}\\) \\(\\implies\\)\u00a0 tan (A + B) = tan 60 \\(\\implies\\)\u00a0 A + B = 60\u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;&#8230;&#8230;(1) Also, tan (A &#8211; B) = \\(1\\over \\sqrt{3}\\) \\(\\implies\\)\u00a0 tan(A &#8211; B) = tan 30 \\(\\implies\\)\u00a0 A &#8211; B = 30\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 &#8230;&#8230;&#8230;&#8230;(2) &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/if-tan-a-b-sqrt3-and-tan-a-b-1over-sqrt3-0-a-b-le-90-a-ge-b-find-a-and-b\/\"> <span class=\"screen-reader-text\">If tan (A + B) = \\(\\sqrt{3}\\) and tan (A &#8211; B) = \\(1\\over \\sqrt{3}\\) ; 0 < A + B \\(\\le\\) 90 ; A \\(\\ge\\) B, find A and B.<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","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>If tan (A + B) = \\(\\sqrt{3}\\) and tan (A - B) = \\(1\\over \\sqrt{3}\\) ; 0 &lt; A + B \\(\\le\\) 90 ; A \\(\\ge\\) B, find A and B. - 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\/if-tan-a-b-sqrt3-and-tan-a-b-1over-sqrt3-0-a-b-le-90-a-ge-b-find-a-and-b\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If tan (A + B) = \\(\\sqrt{3}\\) and tan (A - B) = \\(1\\over \\sqrt{3}\\) ; 0 &lt; A + B \\(\\le\\) 90 ; A \\(\\ge\\) B, find A and B. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : We have, tan (A + B) = (sqrt{3}) (implies)\u00a0 tan (A + B) = tan 60 (implies)\u00a0 A + B = 60\u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;&#8230;&#8230;(1) Also, tan (A &#8211; B) = (1over sqrt{3}) (implies)\u00a0 tan(A &#8211; B) = tan 30 (implies)\u00a0 A &#8211; B = 30\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 &#8230;&#8230;&#8230;&#8230;(2) &hellip; If tan (A + B) = (sqrt{3}) and tan (A &#8211; B) = (1over sqrt{3}) ; 0 &lt; A + B (le) 90 ; A (ge) B, find A and B. Read More &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/if-tan-a-b-sqrt3-and-tan-a-b-1over-sqrt3-0-a-b-le-90-a-ge-b-find-a-and-b\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2022-08-14T18:19:02+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-08-14T18:19:09+00:00\" \/>\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\/if-tan-a-b-sqrt3-and-tan-a-b-1over-sqrt3-0-a-b-le-90-a-ge-b-find-a-and-b\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/if-tan-a-b-sqrt3-and-tan-a-b-1over-sqrt3-0-a-b-le-90-a-ge-b-find-a-and-b\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"If tan (A + B) = \\\\(\\\\sqrt{3}\\\\) and tan (A &#8211; 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0 < A + B \\(\\le\\) 90 ; A \\(\\ge\\) B, find A and B. - 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\/if-tan-a-b-sqrt3-and-tan-a-b-1over-sqrt3-0-a-b-le-90-a-ge-b-find-a-and-b\/","og_locale":"en_US","og_type":"article","og_title":"If tan (A + B) = \\(\\sqrt{3}\\) and tan (A - B) = \\(1\\over \\sqrt{3}\\) ; 0 < A + B \\(\\le\\) 90 ; A \\(\\ge\\) B, find A and B. - Mathemerize","og_description":"Solution : We have, tan (A + B) = (sqrt{3}) (implies)\u00a0 tan (A + B) = tan 60 (implies)\u00a0 A + B = 60\u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8230;&#8230;&#8230;&#8230;(1) Also, tan (A &#8211; B) = (1over sqrt{3}) (implies)\u00a0 tan(A &#8211; B) = tan 30 (implies)\u00a0 A &#8211; B = 30\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 &#8230;&#8230;&#8230;&#8230;(2) &hellip; If tan (A + B) = (sqrt{3}) and tan (A &#8211; B) = (1over sqrt{3}) ; 0 < A + B (le) 90 ; A (ge) B, find A and B. Read More &raquo;","og_url":"https:\/\/mathemerize.com\/if-tan-a-b-sqrt3-and-tan-a-b-1over-sqrt3-0-a-b-le-90-a-ge-b-find-a-and-b\/","og_site_name":"Mathemerize","article_published_time":"2022-08-14T18:19:02+00:00","article_modified_time":"2022-08-14T18:19:09+00:00","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\/if-tan-a-b-sqrt3-and-tan-a-b-1over-sqrt3-0-a-b-le-90-a-ge-b-find-a-and-b\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/if-tan-a-b-sqrt3-and-tan-a-b-1over-sqrt3-0-a-b-le-90-a-ge-b-find-a-and-b\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"If tan (A + B) = \\(\\sqrt{3}\\) and tan (A &#8211; B) = \\(1\\over \\sqrt{3}\\) ; 0 < A + B \\(\\le\\) 90 ; A \\(\\ge\\) B, find A and B.","datePublished":"2022-08-14T18:19:02+00:00","dateModified":"2022-08-14T18:19:09+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/if-tan-a-b-sqrt3-and-tan-a-b-1over-sqrt3-0-a-b-le-90-a-ge-b-find-a-and-b\/"},"wordCount":61,"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\/if-tan-a-b-sqrt3-and-tan-a-b-1over-sqrt3-0-a-b-le-90-a-ge-b-find-a-and-b\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/if-tan-a-b-sqrt3-and-tan-a-b-1over-sqrt3-0-a-b-le-90-a-ge-b-find-a-and-b\/","url":"https:\/\/mathemerize.com\/if-tan-a-b-sqrt3-and-tan-a-b-1over-sqrt3-0-a-b-le-90-a-ge-b-find-a-and-b\/","name":"If tan (A + B) = \\(\\sqrt{3}\\) and tan (A - B) = \\(1\\over \\sqrt{3}\\) ; 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