" 3."(sin x)/(1+sin x)

The value of the definite integral int _(0)^(pi//2) ((1+ sin 3x)/(1+2 sin x)) dx equals to:

Applying logrithmic differentiation find the derivatives of the following functions (a) y=(cos x)^(sin x) (b) y=((3 sqrt(sin 3x))/(1-sin 3x)) (c ) y=sqrt(x-1)/((3sqrt(x+2))^(2)(sqrt(x+3))^(3))

if a=(1+sin x)/(1-cos x+sin x) then (1+cos x+sin x)/(2sin x) is

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 :

int(cos x+3sin x-5dx)/(3(1-sin x)-cos x)

If p = cos x - sin x, q = (1 - sin ^(3) x)/( 1 - sin x) , r = (1 + cos ^(3) x)/( 1 + cos x) what is the value of p + q + r ?

prove that int(cos x)/((sin x-1)(sin x-3))dx=(1)/(2)log((sin x-3)/(sin x-1))+c

If tan((pi)/(4)+(y)/(2))=tan^(3)((pi)/(4)+(x)/(2))* Prove that (sin y)/(sin x)=(3+sin^(2)x)/(1+3sin^(2)x)