Prove that `(cos^3 theta -cos 3 theta)/(cos theta)+ (sin^3 theta+sin3 theta)/(sin theta)=3`.

Prove that : cos3 theta=4 cos^3 theta-3 cos theta .

Prove that : (sin theta)/(1+cos theta) + (1+cos theta)/(sin theta)= 2 cosec theta .

If (cos theta_(1))/(cos theta_(2))+(sin theta_(1))/(sin theta_(2))=(cos theta_(0))/(cos theta_(2))+(sin theta_(0))/(sin theta_(2))=1 , where theta_(1) and theta_(0) do not differ by can even multiple of pi , prove that (cos theta_(1)*cos theta_(0))/(cos^( 2)theta_(2))+(sin theta_(1)*sin theta_(0))/(sin^(2) theta_(2))=-1

Prove that : sin 2 theta= 2sin theta cos theta .

Prove that : sin 3 theta=3 sin theta-4 sin^3 theta .

Verify that [(cos theta, sin theta),(-sin theta, cos theta)] and [(cos theta, - sin theta),(sin theta, cos theta)] are inverse of each other.

Prove that : cos2 theta cos frac (theta)(2)- cos3 theta cos frac (9 theta)(2)= sin 5 theta sin frac (5theta)(2).

Prove that : (1+sin 2 theta-cos 2 theta)/(1+sin 2 theta+ cos 2 theta)= tan theta .

Prove that sin^3theta+cos^3theta=(sintheta+costheta)(1-sinthetacostheta) .

Prove that (sin theta-cos theta+1)/(sin theta+cos theta-1)=1/(sec theta-tan theta) ,using the identity sec^2 theta=1+tan^2 theta .