{"id":20018,"date":"2022-09-09T05:49:35","date_gmt":"2022-09-09T05:49:35","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7557"},"modified":"2022-09-09T05:49:35","modified_gmt":"2022-09-09T05:49:35","slug":"proof-of-reciprocal-identities","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/09\/proof-of-reciprocal-identities\/","title":{"rendered":"Proof of Reciprocal Identities"},"content":{"rendered":"\n<p>Now, that we know the reciprocal identities of trigonometry, let us now prove each one of them using the definition of the basic trigonometric functions. First, we will derive the reciprocal identity of the sine function. Consider a\u00a0right-angled triangle\u00a0ABC with a right angle at C.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/mdr.foobrdigital.com\/wp-content\/uploads\/2022\/09\/reciprocal-identities-proof-02-1633022226.png\" alt=\"\" class=\"wp-image-7558\"\/><\/figure>\n\n\n\n<p>We know that sin \u03b8 = Perpendicular\/Hypotenuse = c\/a&nbsp;and cosec \u03b8 = Hypotenuse\/Perpendicular = a\/c&nbsp;\u21d2 sin \u03b8 is the reciprocal of cosec \u03b8 and cosec \u03b8 is the reciprocal of sin \u03b8. Similarly, we will prove other reciprocal identities. cos \u03b8 = Base\/Hypotenuse = b\/a&nbsp;and cosec \u03b8 = Hypotenuse\/Base = a\/b \u21d2 cos \u03b8 is the reciprocal of sec \u03b8 and sec \u03b8 is the reciprocal of cos \u03b8. tan \u03b8 = sin \u03b8\/cos \u03b8 and cot \u03b8 = cos \u03b8\/sin \u03b8 \u21d2 tan \u03b8 is the reciprocal of cot \u03b8 and cot \u03b8 is the reciprocal of tan \u03b8. Hence, we have<\/p>\n\n\n\n<ul><li>sin \u03b8 is the reciprocal of cosec \u03b8<\/li><li>cosec \u03b8 is the reciprocal of sin \u03b8<\/li><li>cos \u03b8 is the reciprocal of sec \u03b8<\/li><li>sec \u03b8 is the reciprocal of cos \u03b8<\/li><li>tan \u03b8 is the reciprocal of cot \u03b8<\/li><li>cot \u03b8 is the reciprocal of tan \u03b8<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Now, that we know the reciprocal identities of trigonometry, let us now prove each one of them using the definition of the basic trigonometric functions. First, we will derive the reciprocal identity of the sine function. Consider a\u00a0right-angled triangle\u00a0ABC with a right angle at C. We know that sin \u03b8 = Perpendicular\/Hypotenuse = c\/a&nbsp;and cosec [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[375],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/20018"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=20018"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/20018\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=20018"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=20018"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=20018"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}