(a-b)2 <\/sup>= a2<\/sup> \u2013 2ab + b2<\/sup><\/p>\n Similarly, we have identities even in Trigonometry which are mostly used in solving trigonometric equations.<\/p>\n Let us assume any point (x,y) be a point in the first quadrant on an unit circle.<\/p>\n Then by the definitions of trigonometric ratios, we have<\/p>\n Sin t = y; Cost = x; Tan t = y\/x; Cosec t = 1\/y; Sec t = 1\/x; Cot t = x\/y<\/p>\n From these definitions itself, we can derive the following elementary trigonometric identities.<\/em><\/strong><\/p>\n Sin t = 1\/ Cosec t;<\/strong><\/p>\n Cos t = 1\/ Sec t;<\/strong><\/p>\n Tan t = 1\/Cot t;<\/strong><\/p>\n Also, Tant = Sint\/Cost; Cott = Cost\/Sint<\/em><\/strong><\/p>\n Beyond these elementary trigonometric identities, we have some other identities known as Pythagorean identities.<\/em><\/strong><\/p>\n By Pythagoras theorem, we know that, in a right angled triangle the square of the hypotenuseis equal to sum of the squares of the other two sides.<\/p>\n By applying this theorem to the above figure we get.<\/p>\n x2<\/sup> + y2<\/sup> = 1<\/p>\n Cos2<\/sup>t + Sin2<\/sup>t = 1;<\/p>\n By dividing this equation by Cos2<\/sup>t, we get<\/p>\n Cos2<\/sup>t \/ Cos2<\/sup>t \u00a0+ \u00a0Sin2<\/sup>t\/ Cos2<\/sup>t \u00a0= 1\/ Cos2<\/sup>t<\/p>\n 1 + Tan2<\/sup>t= Sec2<\/sup>t;<\/p>\n Again by dividing the same equation by Sin2<\/sup>t, we get<\/p>\n Cos2<\/sup>t\/ Sin2<\/sup>t \u00a0+ \u00a0Sin2<\/sup>t\/ Sin2<\/sup>t = 1\/ Sin2<\/sup>t<\/p>\n Cot2<\/sup>t + 1 = Cosec2<\/sup>t;<\/p>\n Thus we are derived the Pythagorean identities which are listed as follows.<\/p>\n Cos2<\/sup>t + Sin2<\/sup>t = 1;<\/em><\/strong><\/p>\n 1 + Tan2<\/sup>t= Sec2<\/sup>t;<\/em><\/strong><\/p>\n Cot2<\/sup>t + 1 = Cosec2<\/sup>t;<\/em><\/strong><\/p>\n Still need more help with Trigonometry? Take a look at our Trigonometry tutoring services.<\/a><\/p>\n SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Alaska visit: Tutoring in Alaska. <\/a><\/p>\n","protected":false},"excerpt":{"rendered":" An \u00a0identity is a mathematical statement which equates any two mathematical expressions. In algebra we have the following identities which are mostly used in factoring the expressions. (a+b)2 = a2 + 2ab + b2 (a-b)2 = a2 \u2013 2ab + b2 Similarly, we have identities even in Trigonometry which are mostly used in solving trigonometric […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[18],"tags":[573,907,1452,1859,1907],"class_list":["post-4396","post","type-post","status-publish","format-standard","hentry","category-trigonometry","tag-elementary","tag-identity","tag-pythagorean","tag-trigonometric","tag-unit-circle"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/4396","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=4396"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/4396\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=4396"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=4396"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=4396"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/10\/trig-identity1.jpg\" "\\"trig")
<\/a><\/p>\n