Question

(cos x)/(1 + sin x) = (cos(x/2) - 1)/(cos(x/2) + 1)​

Answer 1

(cosx/2 + sinx/2)^2 = (cosx/2)^2 + (sinx/2)^2 + 2*sin(x/2)*cos(x/2)

Since (cos(x))^2 + (sin(x))^2 = 1

Applying the same with substituting x with x/2

the LHS (Left Hand Side) = 1 + 2*sin(x/2)*cos(x/2)

Since 2*sin(x) * cos(x) = sin(2*x)

Then LHS = 1 + 2*sin(x/2)*cos(x/2) = 1 + sin(x) = RHS