Prove tan (θ / 2) = sin θ / (1 + cos θ) for θ in quadrant 1.

We are asked to prove tan (θ / 2) = sin θ / (1 + cos θ). In this case, tan θ is equal to sin θ / cos θ. we can apply this to the equality. sin θ is equal to square root of (1-cos θ) / 2 while cos θ is equal to square root of (1 + cos θ) / 2.

Hence, when we replace cos θ with square root of (1-cos θ) / 2, we can prove already.