" 4.(i) "(sin x)/(1+sin x)

" 4.(i) "int(sin x)/(1-sin^(2)x)dx

Find real x such that (3+2i sin x)/(1-2i sin x) is purely real.

I= int ( sin 2 x)/( 1+ sin^(2) x) dx .

"I=int(sin x)/(1+sin x)*dx

Evaluate: (i) int(sin4x)/(sin2x)dx( ii) int(sin4x)/(cos2x)dx

Evaluate: (i) int(sin4x)/(sin2x)\ dx (ii) int(sin4x)/(cos2x)\ 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 :

(sin x) / (sin2x sin3x) + (sin x) / (sin3x sin4x) + (sin x) / (sin4x sin5x) + .... n

Prove : int sin x sin 2x cos 3x dx = 1/4 ((sin 2x)/2 + (sin 4x)/4 - (sin 6x)/6- x ) + c