If `y="log"(a+b "tan"(x)/(2))/(a-b "tan"(x)/(2))` and `z=(1)/(a^(2)"cos"^(2)(x)/(2)-b^(2) "tan"(x)/(2))`, then show that, `(dy)/(dz)=(ab)/(a^(2)+b^(2))(a^(2)"cot"(x)/(2)-b^(2)"tan"(x)/(2))`.

if g(x)=(x-a)/x+x/(x-b) then show that g((a+b)/2)=(4ab)/(a^2-b^2)

If log(x^2+y^2)=2tan^(-1)(y/x), show that (dy)/(dx)=(x+y)/(x-y)

"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 =cos^(-1)((1-tan^(2) ""(x)/(2))/(1+tan^(2)""(x)/(2))) then find dy/dx ?

If x="tan"(y)/(2)+"log tan"(y)/(2)-2log(1+"tan"(y)/(2)) , show that, (dy)/(dx)=(1)/(2)"sin"(1+sin y+cos y)

If a sin x=b cosx=(2c tan x)/(1-tan^(2)x) , then prove that (a^(2)-b^(2))^(2)=4c^(2)(a^(2)+b^(2)).

If x=(4ab)/(a+b) then show that (x+2b)/(x-2b)+(x+2b)/(x-2b)=2 .

tan^(2)x + cot^(2)x =2

If tan^(-1)sqrt((a^(2)-x^(2))/(a^(2)+x^(2)) + tan^(-1)sqrt((b^(2)-y^(2))/(b^(2)+y^(2)) = (alpha)/(2) , then show that, (x^(4))/(a^(4))-2(x^(2)y^(2))/(a^(2)b^(2))cos alpha+(y^(4))/(b^(4))=sin^(2)alpha

If y= (tan^(-1)x)^2, then show that (1+x^2)^2(d^2y)/(dx^2)+2x(1+x^2)(dy)/(dx) =2 .