If`|x^(2)-1+sin x|=|x^(2)-1|+|sin x|` where x in`[-2 pi,2 pi]`

The value of sin ^(-1)[cos (cos ^(-1)(cos x)+sin ^(-1)(sin x))] where x in((pi)/(2), pi) is

The value of sin^(-1)(cos(cos^(-1)(cos x)+sin^(-1)(sin x))) where x in((pi)/(2),pi), is equal to (pi)/(2)(b)-pi(c)pi (d) -(pi)/(2)

Interval satisfying the inequality log_((1)/(2))((1)/(2)+sin x)<=0 is equal to (where x in[-pi,pi])

Show that tan^-1((cosx)/(1 + sin x)) = pi/4 - x/2 , where x in (-pi/2 , pi/2)

If sin x + sin ((pi)/(8) sqrt((1 - cos 2 x)^(2) + sin ^(2) 2 x)) = 0, x e [(5 pi)/(2), (7 pi)/(2)] , then x is

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

int sqrt((1+sin x))(cos((x)/(2))-sin((x)/(2)))dx=("where "x in(0,pi))[[" (A) "(1+sin x)/(2)+c," (B) "(1+sin x)^(2)+c],[" (C) "(1)/(sqrt(1+sin x)+c),"(D) "sin x+c]]

int _ (- 1) ^ ((3) / (2)) | x sin pi x | dx = [(- x cos pi x) / (pi) + (sin pi x) / (pi ^ (2))] _ (- 1) ^ (1) - [(- x cos pi x) / (pi) + (sin pi x) / (pi ^ (2))] _ (1) ^ ((3) / (2) )