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

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))

Show that (a sin x + b cos x)/(a cos x - b sin x) increases with x.

Find the area bounded by the curves y=(sin^(-1)(sin x)+cos^(-1)(cos x)) and y=(sin^(-1)(sin x)+cos^(-1)(cos x))^(2) for 0<=x<=2 pi

Tan ^(-1) ((a cos x -b sin x)/( b cos x + a sin x ))

If y = tan^(-1) ((a cos x - b sin x)/(b cos x + a sin x)) " then " (dy)/(dx) = ?