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

If A=[(cos^2theta,costheta sintheta),(cos theta sintheta, sin^2theta)] and B=[(cos^2 phi, cos phi sin phi),(cos phisinphi,sin^2phi)], show that AB is zero matrix if theta and phi 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

Prove that the product of the matrices [[cos^2alpha, cosalphasinalpha],[cosalphasinalpha,sin^2alpha]] and [[cos^2beta,cosbetasinbeta],[cosbetasinbeta,sin^beta]] is the null matrix when alpha and beta differ by an odd multiple of pi/ 2.

prove that- sin^2theta/cos^2theta+cos^2theta/sin^2theta=1/ (sin^2thetacos^2theta)-2

Prove that cos^2theta+cos^2thetacot^2theta=cot^2theta

Prove that : (1+sin2 theta-cos 2theta)/(sin theta+cos theta)=2sin theta

Prove that: cos2theta.costheta/2-cos3theta.cos(9theta)/(2)=sin5theta.sin(5theta)/(2)

Inverse of the matrix A=[[cos2theta, -sin2theta], [sin2theta, cos2theta]] is

Inverse of the matrix [[cos2 theta,-sin2 thetasin2 theta,cos2 theta]] is