{"id":6066,"date":"2021-10-05T00:03:31","date_gmt":"2021-10-04T18:33:31","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6066"},"modified":"2021-10-05T00:03:54","modified_gmt":"2021-10-04T18:33:54","slug":"trigonometry-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/trigonometry-examples\/","title":{"rendered":"Trigonometry Examples"},"content":{"rendered":"

Here you will learn some trigonometry examples for better understanding of trigonometry concepts<\/a><\/span>.<\/p>\n\n\n

\n
\n\n \n

Example 1 : <\/span>\\(sin5x + sin2x – sinx\\over {cos5x + 2cos3x + 2cos^x + cosx}\\) is equal to –<\/p>\n

Solution : <\/span>L.H.S. = \\(2sin2xcos3x + sin2x\\over{2cos3x.cos2x + 2cos3x + 2cos^2x}\\)

\n = \\(sin2x[2cos3x+1]\\over {2[cos3x(cos2x+1)+(cos^2x)]}\\)

\n = \\(sin2x[2cos3x+1]\\over {2[cos3x(2cos^2x)+(cos^2x)]}\\)

\n = \\(sin2x[2cos3x+1]\\over {2cos^2x(2cos3x+1)}\\) = tanx<\/p>\n


\n\n \n

Example 2 : <\/span> Prove that : \\(2cos2A+1\\over {2cos2A-1}\\) = tan(\\(60^{\\circ}\\) + A)tan(\\(60^{\\circ}\\) – A)<\/p>\n

Solution : <\/span>R.H.S. = tan(\\(60^{\\circ}\\) + A)tan(\\(60^{\\circ}\\) – A)

\n = (\\(tan60^{\\circ}+tanA\\over {1-tan60^{\\circ}tanA}\\))(\\(tan60^{\\circ}-tanA\\over {1+tan60^{\\circ}tanA}\\))

\n = (\\(\\sqrt{3}+tanA\\over {1-\\sqrt{3}tanA}\\))(\\(\\sqrt{3}-tanA\\over {1+\\sqrt{3}tanA}\\))

\n = \\(3-tan^2A\\over{1-3tan^2A}\\) = \\(3cos^2A-sin^2A\\over {cos^2A-3sin^2A}\\) = \\(2cos^2A+cos^2A-2sin^2A+sin^2A\\over {2cos^2A-2sin^2A-sin^2A-cos^2A}\\)

\n = \\(2(cos^2A-sin^2A)+cos^2A+sin^2A\\over {2(cos^2A-sin^2A)-(sin^2A+cos^2A)}\\)

\n = \\(2cos2A+1\\over {2cos2A-1}\\) = R.H.S<\/p>\n


\n\n \n

Example 3 : <\/span>If A + B + C = \\(3\\pi\\over 2\\), then cos2A + cos2B + cos2C is equal to-<\/p>\n

Solution : <\/span>cos2A + cos2B + cos2C = 2cos(A+B)cos(A-B)+cos2C

\n = 2cos(\\(3\\pi\\over 2\\) – C)cos(A-B) + cos2C   \\(\\because\\)   A + B + C = \\(3\\pi\\over 2\\)

\n = -2sinC cos(A-B) + 1 – 2\\(sin^2C\\) = 1 – 2sinC[cos(A-B)+sinC]

\n = 1 – 2sinC[cos(A-B) + sin(\\(3\\pi\\over 2\\)-(A+B))]

\n = 1 – 2sinC[cos(A-B)-cos(A+B)]

\n = 1 – 4sinA sinB sinC\n <\/p>\n
\n

Practice these given trigonometry examples to test your knowledge on concepts of trigonometry.<\/p>\n \n <\/div>\n <\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn some trigonometry examples for better understanding of trigonometry concepts. Example 1 : \\(sin5x + sin2x – sinx\\over {cos5x + 2cos3x + 2cos^x + cosx}\\) is equal to – Solution : L.H.S. = \\(2sin2xcos3x + sin2x\\over{2cos3x.cos2x + 2cos3x + 2cos^2x}\\) = \\(sin2x[2cos3x+1]\\over {2[cos3x(cos2x+1)+(cos^2x)]}\\) = \\(sin2x[2cos3x+1]\\over {2[cos3x(2cos^2x)+(cos^2x)]}\\) = \\(sin2x[2cos3x+1]\\over {2cos^2x(2cos3x+1)}\\) = tanx Example …<\/p>\n

Trigonometry Examples<\/span> Read More »<\/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":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[28],"tags":[],"yoast_head":"\nTrigonometry Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"Solve these trigonometriy examples to practice and test your knowledge of trigonometry concepts.\" \/>\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\/trigonometry-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Trigonometry Examples - 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