prove that: 1-cos2?/sin2?=tan?

Question

Prove that:

 

1-cos2θ/sin2θ=tanθ

 

Please show workings.

 

Thank you.

Answer 1

Use trigonometric identities

 

 

(1-cos2θ)/(sin2θ)=tanθ

 

(1-[cos²θ - sin²θ])/(2sinθcosθ) = tanθ

 

(1-cos²θ+sin²θ)/(2sinθcosθ) = tanθ

 

(sin²θ+sin²θ)/(2sinθcosθ) = tanθ

 

(2sin²θ)/(2sinθcosθ) = tanθ

 

sinθ/cosθ = tanθ

 

tanθ = tanθ