If `sin theta` is G.M. of `sin phi and cos phi,` then prove that `cos2theta=2cos^2(pi/4+phi)`

If sin theta is G.M. of sin phi and cos phi, then prove that cos 2 theta = 2 cos ^(2) ((pi)/(4) + phi).

If sin theta - sin phi = a and cos theta + cos phi = b then prove that cos(theta + phi) = (a^(2)+b^(2) -2)/2

If sin theta+ sin phi= sqrt3 (cos phi-cos theta) , prove that : sin 3 theta+ sin 3 phi=0 .

If sin theta +sin phi=a and cos theta +cos phi =b then prove cos (theta +phi)=(b^(2)-a^(2))/(b^(2)+a^(2))

If sin 2 theta + sin 2 phi =1/2 and cos 2 theta + cos 2 phi =3/2, then cos ^(2) (theta - phi)=

If sin 2 theta + sin 2 phi =1/2 and cos 2 theta + cos 2 phi =3/2, then cos ^(2) (theta - phi)=

If sin theta+sin phi=sqrt(3)(cos phi-cos theta), prove that sin3 theta+sin3 phi=0

If sin theta+sin phi=sqrt(3)(cos phi-cos theta)), prove that sin3 theta+sin3 phi=0

Prove that sin^2(theta-phi)-sin^2(theta+phi)= -sin2theta sin2phi hence prove that cos2thetacos2phi-sin^2(theta+phi)+sin^2(theta-phi)=cos(2theta+2phi)

If sin 2theta+sin 2phi=1//2 and cos2theta+cos 2phi=3//2 , then cos^(2)(theta-phi)=