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Math Help - Identities

  1. #1
    Junior Member
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    Question Identities

    If cosec A +secA=cosecB+secB , prove that tanA tanB=cot{(A+B)/2}


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  2. #2
    MHF Contributor red_dog's Avatar
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    \frac{1}{\sin A}+\frac{1}{\cos A}=\frac{1}{\sin B}+\frac{1}{\cos B}\Rightarrow

    \Rightarrow\frac{1}{\sin A}-\frac{1}{\sin B}=\frac{1}{\cos B}-\frac{1}{\cos A}\Rightarrow

    \frac{\sin B-\sin A}{\sin A\sin B}=\frac{\cos A-\cos B}{\cos A\cos B}\Rightarrow\frac{\sin A\sin B}{\cos A\cos B}=\frac{\sin B-\sin A}{\cos A-\cos B}\Rightarrow

    \tan A\tan B=\frac{2\sin\frac{B-A}{2}\cos\frac{A+B}{2}}{2\sin\frac{B-A}{2}\sin\frac{A+B}{2}}=\cot\frac{A+B}{2}
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