If `(d^(2))/(d x ^(2))((sin ^(4)x+ sin ^(2)x+1)/(sin ^(2)x + si n x+1))= a sin ^(2) x+b sin x+c ` then the value of `b+c -a` is

If sin ^(2) x + (1)/(4) sin^(2) 3x = sin x sin^(2) 3 x then x =

sin x+sin3x+...+sin(2n-1)x=(sin^(2)nx)/(sin x)

If int sin^(2) xcos^(2) xdx =(1)/(n) [x-(sin 4x)/(4)]+c then the value of n is-

Prove : int sin^(2) x cos 2x dx = 1/4 ( sin 2 x - (sin 4x)/4 - x) + c

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 :

If int(cos^(4)x)/(sin^(2)x)dx=A cot x +B sin 2x +(C)/(2)x+D , then

If int(cos^(4)x)/(sin^(2)x)dx=A cot x +B sin 2x +(C)/(2)x+D , then

Let a= ( 2 sin x )/(1 + sin x + cos x ) and b = ( c )/(1+ sin x ) . Then a = b , if c= ?