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

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

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

Evaluate the following: int frac{cos theta }{cos 3 theta} d theta

Solve the following:Show that (costheta+isintheta)^3=cos3theta+isin3theta

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

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

Prove the following: (frac(sintheta)(1+costheta))=tan(theta/2)

Prove the following: ((tantheta+(1)/(costheta))^2+((tantheta-(1)/(costheta))^2=2(frac(1+sin^2theta)(1-sin^2theta))

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

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