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    ​Find the value of 1−sec⁡2θsin⁡2θ×cos⁡2θ\frac{1 - \sec^2 \theta}{\sin^2 \theta} \times \cos^2 \thetasin2θ1−sec2θ​×cos2θ​​​
    Question

    Find the value of 1sec2θsin2θ×cos2θ\frac{1 - \sec^2 \theta}{\sin^2 \theta} \times \cos^2 \theta​​

    A.

    tanθ

    B.

    ​​​tan2θtan^2⁡θ​​

    C.

    -1

    D.

    1​​

    Correct option is C

    Given: 

    1sec2θsin2θ×cos2θ\frac{1 - \sec^2 \theta}{\sin^2 \theta} \times \cos^2 \theta 

    Formula Used: 

    sec2θ=1+tan2θ\sec^2 \theta = 1 + \tan^2 \theta ​​

    cosθsinθ=cotθ\frac{\cos \theta}{\sin \theta} = \cot \theta  

    Solution: 

    1sec2θsin2θ×cos2θ =(tan2θ)×1tan2θ =1\frac{1 - \sec^2 \theta}{\sin^2 \theta} \times \cos^2 \theta \\ \ \\ = (- \tan^2 \theta )\times \frac{1}{\tan^2 \theta} \\ \ \\ = -1​​

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