`y=tan^(- 1)[sqrt((a-b)/(a+b))tanx/2]`

Find (dy)/(dx) when : y= tan^(-1)[sqrt((a-b)/(a+b))"tan"(x)/(2)]

If y=2/(sqrt(a^(2)-b^(2)))tan^(-1)[sqrt((a-b)/(a+b))"tan"x/2] , prove that dy/dx=1/(a+bcosx),agtbgt0 .

"If "y=(2)/(sqrt(a^(2)-b^(2))){tan^(-1)(sqrt((a-b)/(a+b))tan""(x)/(2))}," then show that "(d^(2)y)/(dx^(2))=(b sin x)/((a+b cos x)^(2)).

If y=2/sqrt(a^2-b^2)tan^-1[sqrt((a-b)/(a+b))tan(x/2)] then (d_2y)/(dx^2)|(x=pi/2)|

If y=2/sqrt(a^2-b^2)tan^-1[sqrt((a-b)/(a+b))tan(x/2)] then (d_2y)/(dx^2)|(=),(x=pi/2):|

If y=2/(sqrt(a^2-b^2)){tan^(-1)sqrt((a-b)/(a+b))tan(x/2)} , then show that (d^2y)/(dx^2)=(bsinx)/((a+bcosx)^2)

If y=2/(sqrt(a^2-b^2))tan^(-1){sqrt((a-b)/(a+b))tan(x/2)} , then show that (d^2y)/(dx^2)=(bsinx)/((a+bcosx)^2)

Prove that : 2tan^(-1)(sqrt((a-b)/(a+b))tan""x/2)=cos^(-1)((acosx+b)/(a+bcosx)) .

A: int (1)/(3+2 cos x)dx=(2)/(sqrt(5))"Tan"^(-1)((1)/(sqrt(5))"tan" (x)/(2))+c R: If a gt b then int (dx)/(a+b cosx)=(2)/(sqrt(a^(2)-b^(2)))Tan^(-1)[(sqrt(a-b))/(a+b)"tan"(x)/(2)]+c