Prove the identity.
(sin^2x)/(1-cosx)^2=(1+cosx)/(1-cos x)

Step-by-step explanation:

We consider the (sin²x)/(1-cos x)² as left hand side (LHS)

While (1+cosx) / (1-cosx) is RHS (Right hand side)

Before proceeding with the equation, we must know some trigonometric and algebraic corollary such as-

Sin²x= 1-cos²x

a²-b²= (a+ b) *(a -b)

(a-b)²= (a- b) *(a-b)

Using these corollaries to our advantage in solving our problem-

From 1 sin²x can be written as 1-cos²x

Similarly, 1-cos²x can be written as 1²-cos²x (in the form of a²-b² and then using the formula 2)

Thus, sin²x can be finally written as (1+cos x) * (1-cos x)

Similarly (1-cos x)² can be written as (1-cos x) * (1-cos x)

Putting the above two steps in the LHS equation-

(1+cos x) *(1-cos x)/ (1-cos x) *(1-cos x)    (common term (1-cos x) gets cancelled out)

LHS= (1+cos x) / (1-cos x)

Hence LHS=RHS

right

step-by-step explanation:

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