Establish the identity 1 cos2 theta1 sin theta sin theta

Establish the identity. 1 - cos^2 theta/1 + sin theta = sin theta Simplify the numerator of the fraction from the left side by applying the appropriate Pythagorean Identity. 1 - squarebox/1 + sin theta (Do not factor.) Factor the numerator of the fraction from the previous step. 1 - squarebox/1 + sin theta The expression from the previous step then simplifies to sin theta using what?

Solution

1 - [cos²/(1 + sin)] = sin

LHS = 1 - [cos²/(1 + sin)] = 1 - [(1 - sin²)/(1 + sin)] = 1 - [(1 - sin)(1 + sin)/(1 + sin)]

= 1 - (1 - sin) = sin = RHS