`(cos x- cos y) ^(2) + (sin x - sin y) ^(2) =4 sin ^(2) "" ( x-y)/(2)`

(cos x + cos y ) ^(2) + (sin x - sin y ) ^(2) = 4 cos ^(2) ""(x + y )/( 2)

Prove that (cos x +cos y)^(2)+(sin x-sin y)^(2)=4 cos^(2) ((x+y)/(2))

cos ^(2) 2x -cos ^(2) 6x = sin 4x sin 8x

(sin x - sin y)/( cos x + cos y) = tan ""(x-y)/(2)

The value of (cos^(4)x+cos^(2)x sin^(2) x + sin^(2)x)/(cos^(2)x+ sin^(2) x cos^(2) x + sin^(4)x) is ____________

sin 3x + sin 2x - sin = 4sin x cos "" x/2 cos "" (3x)/(2)

Prove that ( sin x- sin y )/( cos x + cosy ) =tan (( x-y )/( 2))

y = ( sin x ) /( x^(2))

Prove that (cos 4 x + cos 3 x + cos 2x)/(sin 2x + sin 3 x + sin 4 x ) = cot 2 x .

If x = cos theta cos phi + sin theta sin phi cos psi , y = cos theta sin phi - sin theta cos phi cos psi and z = sin theta sin psi , then x^(2) + y^(2) + z^(2) equals :