If `sin^3xcos3x+cos^3xsin3x=3/8,` then the value of `8sin4x` is__

sin^(5) x cos ^(3) x

Consider the system of equations x cos^(3) y+3x cos y sin^(2) y=14 x sin^(3) y+3x cos^(2) y sin y=13 The value of sin^(2)y + 2cos^(2) y is.

Solve the equation sin^3x.cos3x+cos^3x.sin3x+3/8=0

Period of f(x) = sin 3x cos[3x]-cos 3x sin [3x] (where[] denotes the greatest integer function), is

If sinx+sin^2x=1 , then find the value of cos^(12)x +3cos^(10)x + 3 cos^8x + cos^6x-1

" Let " =|{:(cos x,,sin x,,cosx),( cos 2x,,sin 2x,,2cos 2x),(cos 3x,,sin 3x,,3cos 3x):}| then find the values of f(0) and f' (pi//2) .

If tanx+tan2x+tan3x=tanxtan2xtan3x then value of |sin3x+cos3x| is ___________

In a Delta ABC , if cosA cos B cos C= (sqrt3-1)/(8) and sin A sin B sin C= (3+ sqrt3)/(8) , then The value of tan A + tan B + tan C is

Consider the system of equations x cos^(3) y+3x cos y sin^(2) y=14 x sin^(3) y+3x cos^(2) y sin y=13 The number of values of y in [0, 6pi] is

If xsin^(3) theta +y cos^(3) theta=sin theta cos theta and x sin theta =y cos theta , then prove that x^(2)+y^(2)=1 .