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

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

2sin(theta-phi)=sin(theta+phi)=1

cos 2 (theta+ phi) +4 cos (theta + phi ) sin theta sin phi + 2 sin ^(2) phi=

cos 2 (theta+ phi) +4 cos (theta + phi ) sin theta sin phi + 2 sin ^(2) phi=

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

For any two positive acute angles theta and phi if sin(theta+phi)=k sin(theta-phi) and 33(cos2phi-cos2theta)+cos2thetacos2phi=1

cos 2theta cos 2phi + sin^(2) (theta - phi ) - sin^(2) ( theta + phi) is equal to

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

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