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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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