tan^(-1)((sin2x+cos x))/((cos x-sin2))

The derivative of tan^(-1)((sin x-cos x)/(sin x+cos x)) with respect to (x)/(2), where x in(0,(pi)/(2)) is:

The derivative of tan^(-1)((sin x - cos x)/(sin x + cos x)) , with respect to x/2 , where (x in(0,pi/2)) is

tan^(-1)[(2cos x-3sin x)/(3cos x+2sin x)]

If y = Tan ^(-1) ((cos x- sin x)/(cos x + sin x)) then (d ^(2) y)/(dx ^(2))=

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

Evaluate: (i) int tan^(-1)((sin2x)/(1+cos2x))dx( ii) int cos^(-1)(sin x)dx

Prove that , tan^(-1)((2 sin 2x)/(1+2 cos 2x))-(1)/(2)sin^(-1)((3 sin 2x)/(5+4 cos 2x))=x .

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

The value of the integral int(cos^(3)x+cos^(5)x)/(sin^(2)x+sin^(4)x)dx is (A) sin x-6tan^(-1)(sin x)+C(B)sin x-2(sin x)^(-1)+C(C)sin x-2(sin x)^(-1)+6tan^(-1)(sin x)+C(D)sin x-2(sin x)^(-1)+5tan^(-1)(sin x)+C

(1 + sin 2x + cos 2x )/( cos x + sin x ) = 2 cos x