Prove that if `theta+phi=` constant then `sin theta sin phi` has maximum value at `theta = phi.`

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)

(sin ( theta -phi))/(sin theta sin phi) = cot phi - cot theta.

If theta+phi=pi/3 , then for what value of a sin theta . Sin phi is maximum ?

If sin theta sin phi - cos theta cos phi+1 =0 then the value of 1+ cot theta tan phi is-

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

" 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

" 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

" 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

If theta and phi are acute angles, sin theta=1/2, cos phi= 1/3 , then the value of (theta + phi) is:

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