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CosecA+secA=cosecB+secB then prove that tanA. tanB=cotA+B/2

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CosecA+secA=cosecB+secB then prove that tanA. tanB=cotA+B/2

    • Posted by Riya Raj 6 years, 4 months ago

    CBSE > Class 11 > Mathematics
    • 1 answers

    Aditi Singh 6 years, 4 months ago

    cosecA+secA=cosecB+secBcos⁡ecA+sec⁡A=cos⁡ecB+sec⁡B => cosecA−cosecB=secA−secBcos⁡ecA−cos⁡ecB=sec⁡A−sec⁡B => 1sinA−1sinB=1cosA−1cosB1sin⁡A−1sin⁡B=1cos⁡A−1cos⁡B => sinB−sinAsinA.sinB=cosB−cosAcosA.cosBsin⁡B−sin⁡Asin⁡A.sin⁡B=cos⁡B−cos⁡Acos⁡A.cosB => 2sinB−A2cosB+A2sinA.sinB=2sinB−A2sinB+A2cosA.cosB2sin⁡B−A2cos⁡B+A2sin⁡A.sin⁡B=2sin⁡B−A2sin⁡B+A2cos⁡A.cosB => cosB+A2sinB+A2=sinA.sinBcosA.cosBcos⁡B+A2sin⁡B+A2=sin⁡A.sin⁡Bcos⁡A.cosB => cotB+A2=tanA.tanBcot⁡B+A2=tan⁡A.tan⁡B => tanA.tanB=cotB+A2

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