Question

Establish each identity: 1-2cos^2 Θ/sinΘ cosΘ = tan Θ - cotΘ

Answer 1

We know:
\[
2\cos^2(\theta)-1=\cos(2\theta)
\]So:
\[
1-2\cos^2(\theta)=-(2\cos^2(\theta)-1)=-\cos(2\theta)=\sin^2(\theta)-cos^2(\theta)
\]Try using that.