Simplify `cos(theta+(n-3/2)phi)-cos(theta+(n+3/2)phi))`

Simplify : sin{theta+(n-1/2)phi}+sin{theta+(n+1/2)phi}

3tanthetatanphi=1 , then (cos(theta-phi))/(cos(theta+phi))=?

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

Compute the following: {:[(sin(theta+phi), cos(theta+phi)),(sin(theta - phi),cos(theta-phi))] +[(sin(theta-phi), cos(theta-phi)),(sin(theta+phi), cos(theta+phi))]

If 0

Prove that: cos2 theta*cos2 phi+cos^(2)(theta+phi)-cos^(2)(theta-phi)=cos(2 theta+2 phi)

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

The value of [cos 2 (theta+ phi)+ 4 cos (theta + phi) sin theta sin phi+2 sin ^(2) phi] is-

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

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