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    Simplify (1sin2A−1) where 0<A≤90o.(\frac{1}{sin^2A} - 1) \space where \space 0 < A \leq 90^o.(sin2A1​−1) where 0<A≤9
    Question

    Simplify (1sin2A1) where 0<A90o.(\frac{1}{sin^2A} - 1) \space where \space 0 < A \leq 90^o.​​

    A.

    cot2Acot^2A​​

    B.

    sec2Asec^2A​​

    C.

    tan2Atan^2A​​

    D.

    cos2Acos^2A​​

    Correct option is A

    Given:

     (1sin2A1) where 0<A90o.(\frac{1}{sin^2A} - 1) \space where \space 0 < A \leq 90^o. 

    Formula Used: 

    sin2A+cos2A=1sin^2A + cos^2A = 1​​

    Solution: 

    (1sin2A1)(\frac{1}{sin^2A} - 1)

    =1sin2Asin2A =cos2Asin2A =cot2A= \frac{1-sin^2A }{sin^2A} \\\ \\= \frac{cos^2A}{sin^2A} \\\ \\= cot^2A​​

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