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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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