Precalculus- establishing identities

Question

Establish the identity.  Work on one side only.  ((sinθcosθ)/(cos^2θ-sin^2θ))=((tanθ)/(1-tan^2θ))

Answer 1

use double angle identities

prove (sincos/[cos²-sin²])=tan/(1-tan²)

sin2θ=2sinθcosθ

sin2θ/2=sinθcosθ

cos²-sin²=cos2θ

substitute

(sin2θ/2)/(cos2θ)=

(1/2)(sin2θ)/(cos2θ)=

(1/2)(tan2θ)=

tan2θ=(2tanθ/(1-tan²θ)

(1/2)(2tanθ)/(1-tan²θ)=

tanθ/(1-tan²θ) which was to be proved