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Which of the following is RHS of the equation sin⁡2⁡A1−cos⁡⁡A \frac{\sin^2⁡A}{1-\cos⁡A }1−cos⁡Asin2⁡A​​ =
Question

Which of the following is RHS of the equation sin2A1cosA \frac{\sin^2⁡A}{1-\cos⁡A }​ =

A.

sec A + tan A

B.

cosec A

C.

tan A

D.

cos A + 1

Correct option is D

Given:

sin2A1cosA\frac{sin^2A}{1 - cosA}  

Formula Used: 

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

sin2A=1cos2A\sin^2A = 1 - \cos^2A 

Solution: 

sin2A1cosA\frac{sin^2A}{1 - cosA} ​

1cos2A1cosA\frac{1 - cos^2A}{1 - cosA} 

=  (1+cosA)(1cosA)1cosA\frac{(1 + cosA)(1 - cosA)}{1 - cosA} 

= (1 + cosA) 

The simplified form of the given expression is:  (1 + cosA).

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