`cos x. cos x-sin x.sin x=?`

The function f(x) given by f(x)=(sin 8x cos x-sin6x cos 3x)/(cos x cos2x-sin3x sin 4x) , is

The general solution of the equation 8 cos x cos 2x cos 4x = sin 6x//sin x is

Solve : cos 3x. Cos^(3)x+sin 3x.sin^(3)x=0

Simplify by reducing to a single term : sin (x -y) cos x - cos (x-y) sin x.

Prove that : (sin (x+y))/(sin (x-y) )= (sin x. cos y + cos x . Sin y)/(sin x. cos y-cos x. sin y)

Prove that : (cos 4x sin 3x - cos 2x sin x)/(sin 4x .sin x + cos 6x .cos x) = tan 2x

(1 + sin 2x + cos 2x )/( cos x + sin x ) = 2 cos x

If |cos x + sin x| + | cos x - sin x| = 2 sin x; x in [0,pi] , then maximum integral value of x is :

Let P(x)=cot^(2)x ((1+tanx+tan^(2)x)/(1+cot x+ cot^(2)x))+((cos x-cos 3x+sin3x-sin x)/(2(sin 2x+cos2x)))^(2) . Then, which of the following is (are) correct ?

Prove that: (cos9x-cos5x)/(sin 17 x-sin3x)=\ -(sin2x)/(cos 10 x)