tan^(-1)(sin x+cos x)

int(2sin x)/((3+sin2x))dx is equal to (1)/(2)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+c(1)/(2)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(2sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+c(1)/(4)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+cnone of these

Differentiate the following w.r.t. x (i) cos ^(-1)(sin x) (if) tan ^(-1)(sin x/(1+cos x)) (iii) sin ^(-1)((2^(x+1))/(1+4^x))

If y = tan^(-1)((sin 3x - cos 3x )/(sin 3x + cos 3x))" then" (dy)/(dx) =

integration (tan x)^(1/2) /(sin x*cos x)

1- (sin ^ (2) x) / (1 + cot x) - (cos ^ (2) x) / (1 + tan x) = sin x cos x

1- (sin ^ (2) x) / (1 + cot x) + (cos ^ (2) x) / (1 + tan x) = sin x cos x

tan^(-1)((sin x)/(1+cos x))

tan ^ (- 1) ((sin x) / (1 + cos x))

If y=tan^(-1) ((sin x)/(1-cos x)),"then " dy/dx=

Write in the simplest form : tan^-1 (sin x/(1 + cos x))