If `sin^2 x+|cos x|+|sin x|+1 <=0,` then `x in....`

int_(0)^(pi//2) ( sin x cos x )/( 1+ sin x ) dx is equal to

(cos^(3) x- sin^(2) x)/(cos x - sin x)=(1)/(2) (2 + sin 2x)

int_(0)^(pi//2) ""(sin x - cos x)/( 1-sin x * cos x) dx is equal to

int_(0)^((pi)/(2)) ( sin x - cos x )/( 1+ sin x cos x ) dx = ".............."

Number of solution of the equation sin 2x + cos 2x + sin x + cos x + 1 = 0 In the interval, (0, pi//2) is

Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x )

2tan2x = (cos x + sin x) / (cos x-sin x) - (cos x-sin x) / (cos x + sin x)

int (sin x * e ^ (cos x) - (sin x + cos x) e ^ (sin x + cos x)) / (e ^ (2sin x) -2e ^ (sin x) +1) dx

Prove that (cos x + sin x)/(cos x - sin x) - (cos x - sin x)/(cos x + sin x) = 2 tan x

If sin x+cos x=1+sin x.cos x then x=