To find the exact value of the expression:<\/p>\n\n\n\n
[
\\cos\\left(\\frac{7\\pi}{4} – \\frac{11\\pi}{6}\\right)
]<\/p>\n\n\n\n
Step 1: Compute the Angle Difference<\/h3>\n\n\n\n
We first find the difference between the angles:<\/p>\n\n\n\n
[
\\frac{7\\pi}{4} – \\frac{11\\pi}{6}
]<\/p>\n\n\n\n
To subtract these fractions, we need a common denominator. The least common denominator between 4 and 6 is 12. Rewriting both fractions:<\/p>\n\n\n\n
[
\\frac{7\\pi}{4} = \\frac{21\\pi}{12}, \\quad \\frac{11\\pi}{6} = \\frac{22\\pi}{12}
]<\/p>\n\n\n\n
Now subtract:<\/p>\n\n\n\n
[
\\frac{21\\pi}{12} – \\frac{22\\pi}{12} = \\frac{-\\pi}{12}
]<\/p>\n\n\n\n
Step 2: Use the Cosine Identity<\/h3>\n\n\n\n
We use the identity for cosine of a negative angle:<\/p>\n\n\n\n
[
\\cos(-x) = \\cos(x)
]<\/p>\n\n\n\n
Thus,<\/p>\n\n\n\n
[
\\cos\\left(\\frac{-\\pi}{12}\\right) = \\cos\\left(\\frac{\\pi}{12}\\right)
]<\/p>\n\n\n\n
Step 3: Find the Exact Value of (\\cos(\\pi\/12))<\/h3>\n\n\n\n
Using 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
Let:<\/p>\n\n\n\n
[
A = \\frac{\\pi}{4}, \\quad B = \\frac{\\pi}{6}
]<\/p>\n\n\n\n
[
\\cos\\left(\\frac{\\pi}{12}\\right) = \\cos\\left(\\frac{\\pi}{4} – \\frac{\\pi}{6}\\right)
]<\/p>\n\n\n\n
Using known values:<\/p>\n\n\n\n
[
\\cos \\frac{\\pi}{4} = \\frac{\\sqrt{2}}{2}, \\quad \\cos \\frac{\\pi}{6} = \\frac{\\sqrt{3}}{2}
]<\/p>\n\n\n\n
[
\\sin \\frac{\\pi}{4} = \\frac{\\sqrt{2}}{2}, \\quad \\sin \\frac{\\pi}{6} = \\frac{1}{2}
]<\/p>\n\n\n\n
[
\\cos \\frac{\\pi}{12} = \\left(\\frac{\\sqrt{2}}{2} \\times \\frac{\\sqrt{3}}{2} \\right) + \\left(\\frac{\\sqrt{2}}{2} \\times \\frac{1}{2} \\right)
]<\/p>\n\n\n\n
[
= \\frac{\\sqrt{6}}{4} + \\frac{\\sqrt{2}}{4}
]<\/p>\n\n\n\n
[
= \\frac{\\sqrt{6} + \\sqrt{2}}{4}
]<\/p>\n\n\n\n
Conclusion<\/h3>\n\n\n\n
[
\\cos\\left(\\frac{7\\pi}{4} – \\frac{11\\pi}{6}\\right) = \\frac{\\sqrt{6} + \\sqrt{2}}{4}
]<\/p>\n\n\n\n
Now, I will generate an image representing the solution.<\/p>\n\n\n\n Here is the mathematical diagram illustrating the calculation of (\\cos(7\\pi\/4 – 11\\pi\/6)). It includes the unit circle, labeled angles, the computed angle difference, the cosine identity, and the final exact result. Let me know if you need any modifications!<\/p>\n","protected":false},"excerpt":{"rendered":" Find the exact value of the expression: cos(7pi\/4 – 11pi\/6) The Correct Answer and Explanation is : To find the exact value of the expression: [\\cos\\left(\\frac{7\\pi}{4} – \\frac{11\\pi}{6}\\right)] Step 1: Compute the Angle Difference We first find the difference between the angles: [\\frac{7\\pi}{4} – \\frac{11\\pi}{6}] To subtract these fractions, we need a common denominator. The […]<\/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-195432","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195432","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=195432"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195432\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=195432"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=195432"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=195432"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-1632.png\")
<\/figure>\n\n\n\n