Prove that `(frac(sintheta-2sin^3theta)(2cos^3theta-costheta))=tantheta`

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

Prove that (frac(1+sintheta-costheta)(1+sintheta+costheta))=sqrt(1-costheta)/sqrt(1+costheta)

Solve the following:Prove that (frac(cos^3theta-cos3theta)(costheta))+(frac(sin^3theta+sin3theta)(sintheta))=3

Prove that ((1+cottheta+tantheta)(sintheta-costheta))=(frac(sectheta)(cosec^2theta))-(frac(cosectheta)(sec^2theta))

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

Prove the following: (frac(sin^3theta+cos^3theta)(sintheta+costheta))+(frac(sin^3theta-cos^3theta)(sintheta-costheta))=2

Prove that (frac(1+sintheta)(1+costheta)) + (frac(1-sintheta)(1-costheta)) = 2(cosec^2theta-cottheta)

Prove that sin^6theta+cos^6theta=1-3sin^2thetacos^2theta

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

Prove the following ((1+cottheta+tantheta)(sintheta-costheta))/(sec^3theta-cosec^3theta)=sin^2thetacos^2theta