{"id":195435,"date":"2025-02-28T09:04:09","date_gmt":"2025-02-28T09:04:09","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=195435"},"modified":"2025-02-28T09:04:11","modified_gmt":"2025-02-28T09:04:11","slug":"complete-the-identity-cos-x-11-pi-6","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/28\/complete-the-identity-cos-x-11-pi-6\/","title":{"rendered":"Complete the identity cos (x – 11 pi\/6) ="},"content":{"rendered":"\n
Complete the identity. cos (x – 11 pi\/6) =? A. Squareroot 3\/2 (cos x – sin x) B. 1\/2 (Squareroot 3 cos x – sin x) C. -Squareroot 3\/2 (cos x – sin x) D. -Squareroot 3\/2 (cos x + sin x)<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n
To solve for ( \\cos \\left( x – \\frac{11\\pi}{6} \\right) ), we use the cosine difference identity:<\/p>\n\n\n\n
[ \\cos(A – B) = \\cos A \\cos B + \\sin A \\sin B ]<\/p>\n\n\n\n
Step 1: Identify ( A ) and ( B )<\/h3>\n\n\n\n
\n
Here, ( A = x ) and ( B = \\frac{11\\pi}{6} ).<\/li>\n\n\n\n
We need to find ( \\cos \\frac{11\\pi}{6} ) and ( \\sin \\frac{11\\pi}{6} ).<\/li>\n<\/ul>\n\n\n\n
[ \\cos \\left( x – \\frac{11\\pi}{6} \\right) = \\cos x \\cos \\frac{11\\pi}{6} + \\sin x \\sin \\frac{11\\pi}{6} ]<\/p>\n\n\n\n
[ = \\cos x \\cdot \\frac{\\sqrt{3}}{2} + \\sin x \\cdot \\left(-\\frac{1}{2}\\right) ]<\/p>\n\n\n\n
[ = \\frac{\\sqrt{3}}{2} \\cos x – \\frac{1}{2} \\sin x ]<\/p>\n\n\n\n
Step 4: Compare with Answer Choices<\/h3>\n\n\n\n
This matches:<\/p>\n\n\n\n
[ \\frac{1}{2} \\left( \\sqrt{3} \\cos x – \\sin x \\right) ]<\/p>\n\n\n\n
which is option B<\/strong>.<\/p>\n\n\n\n
Thus, the correct answer is:<\/p>\n\n\n\n
[ \\boxed{B} ]<\/p>\n\n\n\n
Now, I’ll generate an image illustrating this identity.<\/p>\n\n\n\n<\/figure>\n\n\n\n
I’ve provided a visual representation of the cosine difference identity, illustrating the calculations for ( \\cos(x – 11\\pi\/6) ). Let me know if you need any modifications or further explanations!<\/p>\n","protected":false},"excerpt":{"rendered":"
Complete the identity. cos (x – 11 pi\/6) =? A. Squareroot 3\/2 (cos x – sin x) B. 1\/2 (Squareroot 3 cos x – sin x) C. -Squareroot 3\/2 (cos x – sin x) D. -Squareroot 3\/2 (cos x + sin x) The Correct Answer and Explanation is : To solve for ( \\cos \\left( […]<\/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-195435","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195435","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=195435"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195435\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=195435"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=195435"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=195435"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-1633.png\")
<\/figure>\n\n\n\n