{"id":134813,"date":"2023-03-21T16:32:36","date_gmt":"2023-03-21T11:02:36","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=134813"},"modified":"2023-03-21T16:32:36","modified_gmt":"2023-03-21T11:02:36","slug":"prove-that-1tan2-a-1cot%c2%b2a-sec%c2%b2-a-1","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/quiz\/prove-that-1tan2-a-1cot%c2%b2a-sec%c2%b2-a-1","title":{"rendered":"Prove that 1+tan2 A 1+cot\u00b2A sec\u00b2 A-1"},"content":{"rendered":"<h2>Question :Prove that 1+tan2 A 1+cot\u00b2A sec\u00b2 A-1<\/h2>\n<h3>The correct answer :We can start with the left-hand side of the given equation:<\/h3>\n<h3>1 + tan\u00b2A<\/h3>\n<h3>We know that tan\u00b2A + 1 = sec\u00b2A, so we can substitute that in:<\/h3>\n<h3>= sec\u00b2A &#8211; 1 + 1<\/h3>\n<h3>= sec\u00b2A<\/h3>\n<h3>Now we can substitute sec\u00b2A into the right-hand side of the equation:<\/h3>\n<h3>1 + cot\u00b2A * sec\u00b2A &#8211; 1<\/h3>\n<h3>= cot\u00b2A * sec\u00b2A<\/h3>\n<h3>= cos\u00b2A\/sin\u00b2A * 1\/cos\u00b2A (since cotA = cosA\/sinA and secA = 1\/cosA)<\/h3>\n<h3>= 1\/sin\u00b2A<\/h3>\n<h3>= csc\u00b2A<\/h3>\n<h3>Therefore, the left-hand side of the equation simplifies to sec\u00b2A, and the right-hand side simplifies to csc\u00b2A, which are equal. Thus, we have proven that:<\/h3>\n<h3>1 + tan\u00b2A = 1 + cot\u00b2A * sec\u00b2A &#8211; 1<\/h3>\n<h3>or, simplifying further:<\/h3>\n<h3>1 + tan\u00b2A = cot\u00b2A * sec\u00b2A<\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Question :Prove that 1+tan2 A 1+cot\u00b2A sec\u00b2 A-1 The correct answer :We can start with the left-hand side of the given equation: 1 + tan\u00b2A We know that tan\u00b2A + 1 = sec\u00b2A, so we can substitute that in: = sec\u00b2A &#8211; 1 + 1 = sec\u00b2A Now we can substitute sec\u00b2A into the right-hand [&hellip;]<\/p>\n","protected":false},"author":21842,"featured_media":132233,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12119],"tags":[],"class_list":{"0":"post-134813","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-quiz"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/134813","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21842"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=134813"}],"version-history":[{"count":1,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/134813\/revisions"}],"predecessor-version":[{"id":134814,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/134813\/revisions\/134814"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/132233"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=134813"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=134813"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=134813"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}