Prove that the product of matrices `[cos^2thetacosthetasinthetacosthetasinthetasin^2theta]` and `[cos^2varphicosvarphisinvarphicosvarphisinvarphisin^2varphi]` is the null matrix, when `theta` and `varphi` differ by an odd multiple of `pi/2` .

Flind the product of two matrices A =[[cos^(2) theta , cos theta sin theta],[cos theta sin theta ,sin^(2)theta]] B= [[cos^(2) phi,cos phi sin phi],[cos phisin phi,sin^(2)phi]] Show that, AB is the zero matrix if theta and phi differ by an odd multipl of pi/2 .

If theta-phi=pi/2, prove that, [(cos^2 theta,cos theta sin theta),(cos theta sin theta,sin^2 theta)] [(cos^2 phi,cos phi sin phi),(cos phi sin phi,sin^2 phi)]=0

If theta-phi=pi/2, prove that, [(cos^2 theta,cos theta sin theta),(cos theta sin theta,sin^2 theta)] [(cos^2 phi,cos phi sin phi),(cos phi sin phi,sin^2 phi)]=0

Prove : (1+sin2theta-cos2theta)/(1+sin2theta+cos2theta)=tantheta

Prove that (cos theta-sintheta)/(cos theta+sintheta)=sec 2 theta-tan 2theta .

Prove that : cos^3 2theta+3cos2theta=4(cos^6theta-sin^6 theta)

Prove that : sin^(2)theta+cos^(4)theta=cos^(2)theta+sin^(4)theta

Prove: (cos e c\ theta+sintheta)(cos e c\ theta-sintheta)=cot^2theta+cos^2theta

Prove that: 1+cos^2 2theta=2(cos^4theta+sin^4theta)

Prove that: (1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=cot theta