If `3tanthetatanphi=1` , then prove that `2cos(theta+phi) = cos(theta-phi)`

Prove that cos (pi + theta) = - cos theta

If theta + phi = alpha and tan theta = k tan phi , then prove that sin (theta - phi) = (k - 1)/(k + 1) sin alpha .

If theta + phi =alpha and tan theta = k tan phi , then prove that sin(theta - phi) =(k-1)/(k+1) sin alpha .

If tan (phi /2)= sqrt((1+a)/(1-a)) tan"" theta/2," then prove that cos "phi=(cos theta-a)/(1-a cos theta)

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

Prove that: (sin2theta)/(1-cos2theta)=cottheta

If cos theta+sin theta=sqrt(2)cos theta then prove that cos theta-sin theta=sqrt(2)sin theta

If sintheta(1+sin^(2)theta)=cos^(2)theta , then prove that cos^(6)theta-4cos^(2)theta+8cos^(2)theta=4

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