`(1+sinx-cosx)/(1+sinx+cosx) = tan(x/2)`

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

Prove that (1+sinx-cosx)/(1+sinx+cosx) +(1+sinx+cosx)/(1+sinx-cosx) =2 cosec x

Prove that (1+sinx-cosx)/(1+sinx+cosx) +(1+sinx+cosx)/(1+sinx-cosx) =2 cosec x

Solve sinx+cosx=1+sinx.cosx

Prove that (1+sinx-cosx)/(1+sinx+cosx)+(1+sinx+cosx)/(1+sinx-cosx) =2+2"cosec "x

int(2sinx)/((3+sin2x)dxi se q u a lto 1/2ln|(2+sinx-cosx)/(2-sinx+cosx)|-1/(sqrt(2))tan^(-1)((sinx+cosx)/(sqrt(2)))+c 1/2ln|(2+sinx-cosx)/(2-sinx+cosx)|-1/(2sqrt(2))tan^(-1)((sinx+c0sx)/(sqrt(2)))+c 1/4ln|(2+sinx-cosx)/(2-sinx+cosx)|-1/(sqrt(2))tan^(-1)((sinx+c0sx)/(sqrt(2)))+c non eoft h e s e

tan^(-1)((1+sinx)/cosx)=

tan^-1(cosx/(1-sinx))

"Tan"^(-1)(cosx)/(1+sinx)=

If |[cosx, sinx, cosx], [-sinx, cosx, sinx], [-cosx, -sinx, cosx]|=0 , then x=