{"id":7797,"date":"2022-09-20T20:14:28","date_gmt":"2022-09-20T20:14:28","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7797"},"modified":"2022-09-20T20:14:28","modified_gmt":"2022-09-20T20:14:28","slug":"double-angle-formulas-of-cos","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/20\/double-angle-formulas-of-cos\/","title":{"rendered":"Double Angle Formulas of Cos"},"content":{"rendered":"\n<p>The sum formula of cosine function is,<\/p>\n\n\n\n<p>cos (A + B) = cos A cos B &#8211; sin A sin B<\/p>\n\n\n\n<p>When A = B, the above formula becomes,<\/p>\n\n\n\n<p>cos (A + A) = cos A cos A &#8211; sin A sin A<\/p>\n\n\n\n<p>cos 2A = cos<sup>2<\/sup>A &#8211; sin<sup>2<\/sup>A<\/p>\n\n\n\n<p>Let us use this as a base formula to derive two other formulas of cos 2A using the Pythagorean identity sin<sup>2<\/sup>A + cos<sup>2<\/sup>A = 1.<\/p>\n\n\n\n<p>(i)&nbsp;cos 2A = cos<sup>2<\/sup>A \u2212 (1 \u2212 cos<sup>2<\/sup>A) =&nbsp;2cos<sup>2<\/sup>A &#8211; 1<\/p>\n\n\n\n<p>(ii) cos 2A = (1- sin<sup>2<\/sup>A) &#8211; sin<sup>2<\/sup>A = 1 &#8211; 2sin<sup>2<\/sup>A<\/p>\n\n\n\n<p>Now, we will derive the formula of cos 2A in terms of tan using the base formula.<\/p>\n\n\n\n<p>cos2A=cos2A\u2212sin2A=cos2A(1\u2212sin2Acos2A)=1sec2A(1\u2212tan2A)=11+tan2A(1\u2212tan2A)=1\u2212tan2A1+tan2Acos\u20612A=cos2\u2061A\u2212sin2\u2061A=cos2\u2061A(1\u2212sin2\u2061Acos2\u2061A)=1sec2\u2061A(1\u2212tan2\u2061A)=11+tan2\u2061A(1\u2212tan2\u2061A)=1\u2212tan2\u2061A1+tan2\u2061A<\/p>\n\n\n\n<p>Thus, the double angle formulas&nbsp;of the cosine function are:<\/p>\n\n\n\n<p>cos 2A = cos<sup>2<\/sup>A &#8211; sin<sup>2<\/sup>A (or) 2cos<sup>2<\/sup>A &#8211; 1 (or) 1 &#8211; 2sin<sup>2<\/sup>A (or) (1 &#8211; tan<sup>2<\/sup>A) \/&nbsp;(1 +&nbsp;tan<sup>2<\/sup>A)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The sum formula of cosine function is, cos (A + B) = cos A cos B &#8211; sin A sin B When A = B, the above formula becomes, cos (A + A) = cos A cos A &#8211; sin A sin A cos 2A = cos2A &#8211; sin2A Let us use this as a [&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\/7797"}],"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=7797"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7797\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7797"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7797"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7797"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}