If `3cosx + 2cos3x=cosy`, `3sinx + 2sin3x =siny`, then `cos2x` equals

Let P(x)=sqrt(( cosx +cos2x+cos3x)^2+ (sin x + sin 2x+sin3x)^2) then P(x) is equal to

If cosx + cosy + cosz = 0 and sinx + siny + sinz =0 , then show that cos (x-y) + cos(y - z) + cos(z - x) = - 3/2.

If cosx+cosy+cosz=sinx+siny+sinz=0" then "cos(x-y)=

If f(x) = \begin{vmatrix} cos2x & cos2x & sin2x \\ -cosx & cosx & -sinx\\ sinx & sinx & cosx \end{vmatrix} then

If (4cos^(2)x -2 sinx -3) sin x = 0 , then x is equal to (n in Z)

If f(x) = |{:( cos (2x) ,, cos ( 2x ) ,, sin ( 2x) ), ( - cos x,, cosx ,, - sin x ), ( sinx,, sin x,, cos x ):}| , then

If cosx+cosy+cosz=sinx+siny+sinz=0" then "cos(x-y)= (a) 0 (b) -1/2 (c) 2 (d) 1

Solve sin x-3 sin 2x + sin 3x = cos x -3 cos 2x + cos 3x .

if x and y are acute angles such that cosx + cosy = 3/2 and sinx + siny = 3/4 then sin(x+y)=

The number of solution of the equation sin^(3)x cos x+sin^(2)x cos^(2)x+cos^(3)x sin x=1 in the interval [0, 2pi] is equal to