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

If y=log("tan"(x)/(2))+sin^(-1)(cosx) , then the value of (dy)/(dx) is -

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

If tan y = (tan x+sec x-1)/(tanx -sec x+1) show that (dy)/(dx) = 1/2

If tan y=(tan x+sec x-1)/(tan x-sec x+1), " show that, " (dy)/(dx)=(1)/(2) .

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 y= tan^(-1)((a cos x-b sin x)/(b cos x+a sin x))" show that, " (dy)/(dx)= -1 .

If x=sqrt(a^(sin^(-1)t)" and "y=sqrt(a^(cos^(-1)t) show that (dy)/(dx)=-(y)/(x) .

If x=sqrt(a^(sin^(-1)t)), y= sqrt(a^(cos^(-1)t)) , show that (dy)/(dx)= -(y)/(x) .

2 tan ^(-1) (Cos x) = tan ^(-1) (2 "cosec"x)

If x^2 = a^(sin^(-1)t) and y^2= a^(cos^(-1)t) then show that (dy)/(dx)=-y/x .