{"id":7812,"date":"2022-09-20T20:35:52","date_gmt":"2022-09-20T20:35:52","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7812"},"modified":"2022-09-20T20:35:52","modified_gmt":"2022-09-20T20:35:52","slug":"half-angle-formula-of-tan-derivation","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/20\/half-angle-formula-of-tan-derivation\/","title":{"rendered":"Half Angle Formula of Tan Derivation"},"content":{"rendered":"\n<p>We know that tan (A\/2) = [sin (A\/2)] \/ [cos (A\/2)]<\/p>\n\n\n\n<p>From the half angle formulas of sin and cos,<\/p>\n\n\n\n<p>tan (A\/2) = [\u00b1\u221a(1 &#8211; cos A)\/2] \/ [\u00b1\u221a(1 + cos A)\/2]<\/p>\n\n\n\n<p>=&nbsp;<strong>\u00b1\u221a[(1 &#8211; cos A)&nbsp;\/ (1 + cos A)]<\/strong><\/p>\n\n\n\n<p>This is one of the formulas of tan (A\/2). Let us derive the other two formulas by&nbsp;<a href=\"https:\/\/www.cuemath.com\/numbers\/rationalize-the-denominator\/\">rationalizing the denominator<\/a>&nbsp;here.<\/p>\n\n\n\n<p>tan (A\/2) = \u00b1\u221a[(1 &#8211; cos A) \/ (1 + cos A)] \u00d7 \u221a[(1 &#8211; cos A) \/ (1 &#8211; cos A)]<\/p>\n\n\n\n<p>= \u221a[(1 &#8211; cos A)<sup>2<\/sup>&nbsp;\/ (1 &#8211; cos<sup>2<\/sup>A)]<\/p>\n\n\n\n<p>= \u221a[(1 &#8211; cos A)<sup>2<\/sup>\/ sin<sup>2<\/sup>A]<\/p>\n\n\n\n<p>=&nbsp;<strong>(1 &#8211; cos A) \/ sin A<\/strong><\/p>\n\n\n\n<p>This is the second formula of tan (A\/2). To derive another formula, let us multiply and divide the above formula by (1 + cos A). Then we get<\/p>\n\n\n\n<p>tan (A\/2) = [(1 &#8211; cos A) \/ sin A] \u00d7 [(1 + cos A) \/ (1 + cos A)]<\/p>\n\n\n\n<p>= (1 &#8211; cos<sup>2<\/sup>A) \/ [sin A (1 + cos A)]<\/p>\n\n\n\n<p>= sin<sup>2<\/sup>A \/ [sin A (1 + cos A)]<\/p>\n\n\n\n<p>=&nbsp;<strong>sin A \/ (1 + cos A)<\/strong><\/p>\n\n\n\n<p>Thus, tan (A\/2) = \u00b1\u221a[(1 &#8211; cos A) \/ (1 + cos A)] = (1 &#8211; cos A) \/ sin A = sin A \/ (1 + cos A).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We know that tan (A\/2) = [sin (A\/2)] \/ [cos (A\/2)] From the half angle formulas of sin and cos, tan (A\/2) = [\u00b1\u221a(1 &#8211; cos A)\/2] \/ [\u00b1\u221a(1 + cos A)\/2] =&nbsp;\u00b1\u221a[(1 &#8211; cos A)&nbsp;\/ (1 + cos A)] This is one of the formulas of tan (A\/2). Let us derive the other two [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[229],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7812"}],"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=7812"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7812\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7812"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7812"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7812"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}