If `theta + phi = 60^(@)`, show that, `sin (120^(@) - theta) = cos (30^(@) - phi)`.

If sin (30 ^(@) - theta) = cos (60 ^(@) + phi) , then

If theta+phi=60^@ ,then show that sin(120^@-theta)=cos(30^@-phi)

If" " tan^(2) theta = 1 + 2 tan^(2) phi, "show that", cos 2theta + sin^(2) phi = 0.

Prove that cos 2 theta cos 2 phi + sin ^(2) ( theta - phi) -sin ^(2) (theta + phi) = cos ( 2 theta + 2 phi).

If 2 tan theta = cot phi, "show that" cos(theta - phi) = 3 cos ( theta + phi).

If " " tan theta = 1/7 " and " tan phi = 1/3 " show that", cos 2 theta = sin 4phi

If tan^2 theta=2 tan^2 phi+1 , show that cos 2 theta+ sin^2 phi=0 .

If sin theta = k sin (theta + phi),"show that", tan(theta + phi) = (sin phi)/(cos phi -k).

If sin theta+ sin phi = a, cos theta + cos phi = b, find the value of sin ( theta+phi) and cos 2theta + cos 2phi where |b|>|a|

If sin theta=k sin(theta+phi), show that tan(theta+phi)=(sin phi)/(cos phi-k)