Prove the following:`(frac(1-cos2theta+sin2theta)(1+cos2theta+sin2theta))=tantheta`

Prove the following: cottheta(1-cos2theta)=sin2theta

Prove the following: (frac(1-cos2theta)(1+cos2theta))=tan^2theta

(sintheta+sin 2theta)/(1+costheta+cos2theta)=

Prove the following: sqrt(frac(1-cos2theta)(1+cos2theta))=tantheta

Prove the following: (frac(cos2theta)(1+sin2theta))=tan(pi/4-0)

|(sin^2theta,cos^2theta),(cos^2theta,sin^2theta)|=

Prove the following: cos^4theta-sin^4theta+1=2cos^2theta

Prove the following: sin^4theta+cos^4theta=1-2sin^2thetacos^2theta

2cos^2theta-2sin^2theta=1 then theta =

Use De Moivers theorem and simplify the following: frac{(cos 2theta + i sin 2theta)^7}{(cos 4theta + i sin 4theta)^3}