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

(sin 3x + sin x ) sin x + (cos 3x - cos x) cos x =0

Solve sin x=0 and ( sin x )/(cos ""(x)/2 cos ""(3x)/2)=0 and show their solutions are different .

sin 3 x + 2 csin 4x + sin 6x = 4 cos ^(2) x sin 4x

((sin 7x + sin 5x ) +(sin 9x + sin 3x))/( (cos 7x + cos 5x ) + (cos 9x + cos 3x ))= tan 6x

Prove that (sin 5x - 2 sin 3x + sin x)/(cos 5 x - cos x)= tan x

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

Find int sin 2x.cos 3x dx .

If f(x) = |(sin x + sin 2x + sin 3x, sin 2x , sin 3x),(3 + 4 sin x, 3, 4 sin x),(1 + sin x, sin x, 1)| then the value of int_0^(-pi//2) f(x) dx equals :

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

The general solution of sinx - 3sin2x + sin3x = cosx - 3cos2x + cos3x is :