To evaluate the given expression:cos\u2061(70\u2218)sin\u2061(20\u2218)=cos\u2061(59\u2218)\u00d7csc\u2061(31\u2218)\\frac{\\cos(70^\\circ)}{\\sin(20^\\circ)} = \\cos(59^\\circ) \\times \\csc(31^\\circ)sin(20\u2218)cos(70\u2218)\u200b=cos(59\u2218)\u00d7csc(31\u2218)<\/p>\n\n\n\n
We will break down each part and verify if the two sides are equal.<\/p>\n\n\n\n
Step 1: Simplify Left-Hand Side<\/h3>\n\n\n\n
First, we simplify the left-hand side, which is:cos\u2061(70\u2218)sin\u2061(20\u2218)\\frac{\\cos(70^\\circ)}{\\sin(20^\\circ)}sin(20\u2218)cos(70\u2218)\u200b<\/p>\n\n\n\n
Recall the trigonometric identity:cos\u2061(70\u2218)=sin\u2061(20\u2218)\\cos(70^\\circ) = \\sin(20^\\circ)cos(70\u2218)=sin(20\u2218)<\/p>\n\n\n\n
This is because of the complementary angle identity, which states that:cos\u2061(\u03b8)=sin\u2061(90\u2218\u2212\u03b8)\\cos(\\theta) = \\sin(90^\\circ – \\theta)cos(\u03b8)=sin(90\u2218\u2212\u03b8)<\/p>\n\n\n\n
Thus, we have:cos\u2061(70\u2218)sin\u2061(20\u2218)=sin\u2061(20\u2218)sin\u2061(20\u2218)=1\\frac{\\cos(70^\\circ)}{\\sin(20^\\circ)} = \\frac{\\sin(20^\\circ)}{\\sin(20^\\circ)} = 1sin(20\u2218)cos(70\u2218)\u200b=sin(20\u2218)sin(20\u2218)\u200b=1<\/p>\n\n\n\n
Step 2: Simplify Right-Hand Side<\/h3>\n\n\n\n
Now, simplify the right-hand side, which is:cos\u2061(59\u2218)\u00d7csc\u2061(31\u2218)\\cos(59^\\circ) \\times \\csc(31^\\circ)cos(59\u2218)\u00d7csc(31\u2218)<\/p>\n\n\n\n
Recall that:csc\u2061(\u03b8)=1sin\u2061(\u03b8)\\csc(\\theta) = \\frac{1}{\\sin(\\theta)}csc(\u03b8)=sin(\u03b8)1\u200b<\/p>\n\n\n\n
So, we have:cos\u2061(59\u2218)\u00d7csc\u2061(31\u2218)=cos\u2061(59\u2218)\u00d71sin\u2061(31\u2218)\\cos(59^\\circ) \\times \\csc(31^\\circ) = \\cos(59^\\circ) \\times \\frac{1}{\\sin(31^\\circ)}cos(59\u2218)\u00d7csc(31\u2218)=cos(59\u2218)\u00d7sin(31\u2218)1\u200b<\/p>\n\n\n\n
Using the complementary angle identity again, we know:cos\u2061(59\u2218)=sin\u2061(31\u2218)\\cos(59^\\circ) = \\sin(31^\\circ)cos(59\u2218)=sin(31\u2218)<\/p>\n\n\n\n
Thus:cos\u2061(59\u2218)\u00d71sin\u2061(31\u2218)=sin\u2061(31\u2218)\u00d71sin\u2061(31\u2218)=1\\cos(59^\\circ) \\times \\frac{1}{\\sin(31^\\circ)} = \\sin(31^\\circ) \\times \\frac{1}{\\sin(31^\\circ)} = 1cos(59\u2218)\u00d7sin(31\u2218)1\u200b=sin(31\u2218)\u00d7sin(31\u2218)1\u200b=1<\/p>\n\n\n\n
Step 3: Conclusion<\/h3>\n\n\n\n
Both the left-hand side and right-hand side simplify to 1:cos\u2061(70\u2218)sin\u2061(20\u2218)=cos\u2061(59\u2218)\u00d7csc\u2061(31\u2218)=1\\frac{\\cos(70^\\circ)}{\\sin(20^\\circ)} = \\cos(59^\\circ) \\times \\csc(31^\\circ) = 1sin(20\u2218)cos(70\u2218)\u200b=cos(59\u2218)\u00d7csc(31\u2218)=1<\/p>\n\n\n\n
Therefore, the given equation is true<\/strong>.<\/p>\n\n\n\n Evaluate : cos( 70 degree ) \/ sin ( 20 degree ) = cos ( 59 degree ) \u00d7 cosec (31 degree ). The Correct Answer and Explanation is: To evaluate the given expression:cos\u2061(70\u2218)sin\u2061(20\u2218)=cos\u2061(59\u2218)\u00d7csc\u2061(31\u2218)\\frac{\\cos(70^\\circ)}{\\sin(20^\\circ)} = \\cos(59^\\circ) \\times \\csc(31^\\circ)sin(20\u2218)cos(70\u2218)\u200b=cos(59\u2218)\u00d7csc(31\u2218) We will break down each part and verify if the two sides are equal. Step 1: Simplify […]<\/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-264743","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/264743","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=264743"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/264743\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=264743"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=264743"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=264743"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1407.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"