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