Verify the identity. No calculator.

Question

Verify the identity.

1−cos2𝜃/sin2𝜃 = tan𝜃

Please show workings.

 

Thank you.

Answer 1

(1 - cos2θ) / sin2θ = (1 - (2cos²θ - 1)) / (2sinθcosθ) =

(2 - 2cos²θ) / (2sinθcosθ) = (1 - cos²θ) / (sinθcosθ) = sin²θ / (sinθcosθ) = sinθ / cosθ = tanθ

Answer 2

Use double-angle formula to convert.