Question

cosx/(1 + sinx).dx
Integrate the function

Answer 1

HELLO DEAR,

GIVEN function is integral of sinx/(1+cosx).dx

we know:- (1 + cosx) = 2cos²(x/2),
cosx = cos²(x/2) - sin²(x/2)

NOW, $\sf{\int{\frac{cos^2(x/2)- sin^2(x/2)}{2cos^2(x/2)}}\,dx}$

=$\sf{1/2[\int{(1-tan^2(x/2))}\,dx]}$

=$\sf{1/2[x-\int{(sec^2(x/2)-1)}\,dx]}$

=$\sf{1/2[x-2tan(x/2)+x]+c}$

=$\sf{x-tan(x/2)+c}$

I HOPE ITS HELP YOU DEAR,
THANKS