Question

Siddh kijiye cosA/1-tanA+sinA/1-1-cotA=sinA+cosA​

Answer 1

How do i prove the following identity, (cos A)/(1-tan A) +(sin A)/(1 - cot A) = sin A + cos A?

Let us start with the equation: (cos A)/(1-tan A) + (sin A)/(1 - cot A)

= sin A + cos A

LHS = (cos A)/(1-tan A) + (sin A)/(1 - cot A), or

= (cos A)/(1 - sin A/cos A) + (sin A)/(1 - cos A/ sin A), or

= (cos A)/[(cos A - sin A)/cos A] + (sin A)/[(sin A - cos A)/sin A], or

= (cos^2 A)/(cos A - sin A) + (sin^2 A)/(sin A - cos A), or

= (cos^2 A)/(cos A - sin A) - (sin^2 A)/(cos A - sin A), or

= [(cos^2 A)- (sin^2 A)/[(cos A - sin A)], or

= [(cos A + sin A)(cos A - sin A)]/(cos A - sin A), or

= (cos A + sin A), or

= sin A+cos A = RHS. Proved.

Step-by-step explanation:

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