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

cos2thetacos2phi+sin^2(theta-phi)-sin^2(theta+phi)=

(sin (theta+phi) -2 sintheta+ sin (theta-phi))/( cos(theta+phi) -2 costheta+ cos (theta-phi))= tan theta

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

(sin (theta + phi))/( sin theta cos phi) = cot theta tan phi +1.

If 0 lt theta , phi lt pi and 8 cos theta cos phi cos (theta + phi)+1=0 find theta and phi

If sin theta+sin2theta+sin3theta=sin alpha and cos theta+cos 2theta+cos3theta=cos alpha , then theta is equal to

" If "|{:(sin theta cos phi,,sin theta sin phi,,cos theta),(cos theta cos phi,, cos theta sin phi,,-sin theta),(-sin theta sin phi,,sin theta cos phi,,theta):}| then

The roots of the equation |(3x^(2),x^(2) + x cos theta + cos^(2) theta ,x^(2) + x sin theta + sin^(2) theta),(x^(2) + x cos theta + cos^(2) theta,3 cos^(2) theta,1 + (sin 2 theta)/(2)),(x^(2) + x sin theta + sin^(2) theta,1 + (sin 2 theta)/(2),3 sin^(2) theta)| = 0

Statement I If 2 cos theta + sin theta=1(theta != (pi)/(2)) then the value of 7 cos theta + 6 sin theta is 2. Statement II If cos 2theta-sin theta=1/2, 0 lt theta lt pi/2 , then sin theta+cos 6 theta = 0 .

(sin theta + sin 2 theta)/( 1 + cos theta + cos 2 theta) = tan theta.