Write Sin 195 \u00b0Cos 83\u00ba – Cos 195 \u00b0Sin 83\u00b0 As The Sine Of A Single Angle. 57 7a 15. Find The Exact Value Of Cos COS 12 12 570 7\u03c0 – Sin -Sin 12 12 Using A Sum Or Difference Formula. 16. Use A Double Angle Formula To Rewrite 18sin3xcos3x.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To simplify this expression, we can use the sine addition formula<\/strong>, which is:<\/p>\n\n\n\n [ If we rearrange the terms in your expression, we see it follows the same structure as the sine addition formula, but with a minus sign:<\/p>\n\n\n\n [ This matches the form of the sine of a difference formula:<\/p>\n\n\n\n [ Thus, we can rewrite the expression as:<\/p>\n\n\n\n [ Simplifying:<\/p>\n\n\n\n [ We can use the sum or difference formula for cosine and sine. First, express the angles in radians. We are dealing with ( \\frac{7\\pi}{12} ), which can be split into easier angles:<\/p>\n\n\n\n [ We can apply the sine and cosine sum formulas:<\/p>\n\n\n\n [ For ( \\cos\\left(\\frac{7\\pi}{12}\\right) – \\sin\\left(\\frac{7\\pi}{12}\\right) ), we can try rewriting it in terms of the sum or difference of trigonometric functions and proceed with substitution. The exact calculation would involve the values for ( \\sin(\\frac{\\pi}{4}) ), ( \\cos(\\frac{\\pi}{6}) ), and so on.<\/p>\n\n\n\n The double angle identity for sine is:<\/p>\n\n\n\n [ In this case, we want to use this identity for ( \\sin(6x) ), since ( 3x ) is half of ( 6x ):<\/p>\n\n\n\n [ Thus, the expression simplifies to:<\/p>\n\n\n\n [ By applying these formulas, we simplify trigonometric expressions and make solving more complex equations easier.<\/p>\n","protected":false},"excerpt":{"rendered":" Write Sin 195 \u00b0Cos 83\u00ba – Cos 195 \u00b0Sin 83\u00b0 As The Sine Of A Single Angle. 57 7a 15. Find The Exact Value Of Cos COS 12 12 570 7\u03c0 – Sin -Sin 12 12 Using A Sum Or Difference Formula. 16. Use A Double Angle Formula To Rewrite 18sin3xcos3x. The Correct Answer and […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","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":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-183134","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183134","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=183134"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183134\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=183134"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=183134"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=183134"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Problem 1: Write ( \\sin(195^\\circ) \\cos(83^\\circ) – \\cos(195^\\circ) \\sin(83^\\circ) ) as the sine of a single angle<\/h3>\n\n\n\n
\\sin(A + B) = \\sin(A)\\cos(B) + \\cos(A)\\sin(B)
]<\/p>\n\n\n\n
\\sin(195^\\circ) \\cos(83^\\circ) – \\cos(195^\\circ) \\sin(83^\\circ)
]<\/p>\n\n\n\n
\\sin(A – B) = \\sin(A)\\cos(B) – \\cos(A)\\sin(B)
]<\/p>\n\n\n\n
\\sin(195^\\circ – 83^\\circ)
]<\/p>\n\n\n\n
\\sin(195^\\circ – 83^\\circ) = \\sin(112^\\circ)
]<\/p>\n\n\n\nProblem 2: Find the exact value of ( \\cos\\left(\\frac{7\\pi}{12}\\right) – \\sin\\left(\\frac{7\\pi}{12}\\right) )<\/h3>\n\n\n\n
\\frac{7\\pi}{12} = \\frac{\\pi}{4} + \\frac{\\pi}{6}
]<\/p>\n\n\n\n
\\cos(A + B) = \\cos(A)\\cos(B) – \\sin(A)\\sin(B)
]<\/p>\n\n\n\nProblem 3: Use a Double Angle Formula to rewrite ( 18\\sin(3x)\\cos(3x) )<\/h3>\n\n\n\n
\\sin(2A) = 2 \\sin(A) \\cos(A)
]<\/p>\n\n\n\n
18 \\sin(3x) \\cos(3x) = 9 \\cdot 2 \\sin(3x) \\cos(3x) = 9 \\sin(6x)
]<\/p>\n\n\n\n
18 \\sin(3x) \\cos(3x) = 9 \\sin(6x)
]<\/p>\n\n\n\nExplanation of the Concepts:<\/h3>\n\n\n\n
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