" 1) "sin^(-1)[(a+b cos x)/(b+a cos x)]

Differentiate sin^(-1)((a+b cos x)/(b+a cos x)),b>a with respect to x:

If y=sin^(-1)((a+b cos x)/(b+a cos x)), prove that (dy)/(dx)=-(sqrt(b^(2)-a^(2)))/(b+a cos x)

Differentiate the following functions with respect to x:log(sec x+tan x)( ii) e^(x sin x)sin^(-1)(x^(3))(iv)sin^(-1)((a+b cos x)/(b+a cos x)),b>a

Simplify tan^(-1)[(a cos x -b sin x)/( b cos x +a sin x)] if a/b tan x gt -1

Simplify tan^(-1)[(a cos x -b sin x)/( b cos x +a sin x)] if a/b tan x gt -1

Simplify tan^(-1)[(a cos x-b sin x)/(b cos x+a sin x)], if (a)/(b)tan x>-1

Simplify tan ^(-1)[(a cos x-b sin x)/(b cos x+a sin x)] if, a/b tan xgt(-1)

If y=(1)/(sqrt(a^(2)-b^(2)))cos^(-1)((a cos x+b)/(a+b cos x)), then (d^(2)y)/(dx^(2))=(i)(b sin x)/((a+b cos x)^(2))( ii) -(b sin x)/((a+b cos x)^(2))( iii) (b cos x)/((a+b cos x)^(2))( iii) -(b cos x)/((a+b cos x)^(2))

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