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| 1. |
CosecA+secA=cosecB+secB then prove that tanA. tanB=cotA+B/2 |
| Answer» cosecA+secA=cosecB+secBcos\u2061ecA+sec\u2061A=cos\u2061ecB+sec\u2061B=> cosecA−cosecB=secA−secBcos\u2061ecA−cos\u2061ecB=sec\u2061A−sec\u2061B=> 1sinA−1sinB=1cosA−1cosB1sin\u2061A−1sin\u2061B=1cos\u2061A−1cos\u2061B=> sinB−sinAsinA.sinB=cosB−cosAcosA.cosBsin\u2061B−sin\u2061Asin\u2061A.sin\u2061B=cos\u2061B−cos\u2061Acos\u2061A.cosB=> 2sinB−A2cosB+A2sinA.sinB=2sinB−A2sinB+A2cosA.cosB2sin\u2061B−A2cos\u2061B+A2sin\u2061A.sin\u2061B=2sin\u2061B−A2sin\u2061B+A2cos\u2061A.cosB=> cosB+A2sinB+A2=sinA.sinBcosA.cosBcos\u2061B+A2sin\u2061B+A2=sin\u2061A.sin\u2061Bcos\u2061A.cosB=> cotB+A2=tanA.tanBcot\u2061B+A2=tan\u2061A.tan\u2061B=> tanA.tanB=cotB+A2 | |