{"id":225577,"date":"2025-06-04T10:17:49","date_gmt":"2025-06-04T10:17:49","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225577"},"modified":"2025-06-04T10:17:51","modified_gmt":"2025-06-04T10:17:51","slug":"sin-c-c","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/sin-c-c\/","title":{"rendered":"sin C C"},"content":{"rendered":"\n

sin C C. cos A = cos C D. cos A = sin B
Select the true statement about triangle ABC. A. cos A = tan C B. cos A = sin C C. cos A = cos C D. cos A = sin B<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct answer is: D. cos A = sin B<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/h3>\n\n\n\n

In any triangle \u25b3ABC\\triangle ABC, the relationship between angles and trigonometric functions is governed by the cofunction identities<\/strong> and the angle sum property<\/strong> of triangles. The sum of interior angles in any triangle is always: A+B+C=180\u2218A + B + C = 180^\\circ<\/p>\n\n\n\n

This means: A+B=180\u2218\u2212CA + B = 180^\\circ – C<\/p>\n\n\n\n

From trigonometric cofunction identities, we know: sin\u2061\u03b8=cos\u2061(90\u2218\u2212\u03b8)andcos\u2061\u03b8=sin\u2061(90\u2218\u2212\u03b8)\\sin \\theta = \\cos (90^\\circ – \\theta) \\quad \\text{and} \\quad \\cos \\theta = \\sin (90^\\circ – \\theta)<\/p>\n\n\n\n

Let\u2019s apply this identity to angles in triangle ABC. Since: A+B=180\u2218\u2212CA + B = 180^\\circ – C<\/p>\n\n\n\n

Then, it follows that: B=180\u2218\u2212C\u2212AB = 180^\\circ – C – A<\/p>\n\n\n\n

Now consider: cos\u2061A=sin\u2061(90\u2218\u2212A)\\cos A = \\sin (90^\\circ – A)<\/p>\n\n\n\n

But in a triangle, if angle B = 90\u00b0 – A, then: cos\u2061A=sin\u2061B\\cos A = \\sin B<\/p>\n\n\n\n

This is exactly what is given in option D: cos A = sin B<\/strong>, making it the true statement.<\/p>\n\n\n\n

\n\n\n\n

Why the other options are incorrect:<\/h3>\n\n\n\n
    \n
  • A. cos A = tan C<\/strong>
    This is not a standard trigonometric identity in triangles. Cosine and tangent relate differently and this equality is not generally true for arbitrary triangle angles.<\/li>\n\n\n\n
  • B. cos A = sin C<\/strong>
    Only true if A+C=90\u2218A + C = 90^\\circ, which is not always the case in every triangle.<\/li>\n\n\n\n
  • C. cos A = cos C<\/strong>
    This would imply that A=CA = C, which is only true for an isosceles triangle where two angles are equal. This is not universally true.<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    Conclusion:<\/h3>\n\n\n\n

    The only universally valid trigonometric identity among the options, applicable to any triangle<\/strong>, is cos A = sin B<\/strong>, due to cofunction identities and the triangle angle sum property.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    sin C C. cos A = cos C D. cos A = sin BSelect the true statement about triangle ABC. A. cos A = tan C B. cos A = sin C C. cos A = cos C D. cos A = sin B The Correct Answer and Explanation is: The correct answer is: D. […]<\/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-225577","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225577","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=225577"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225577\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225577"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225577"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225577"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}