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

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)

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))

(b) tan^(-1)((1-cos x)/(sin x))

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

y=tan^(-1)((a cos x-b sin x)/(b cos x+a sin x)), where -(pi)/(2) -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