If `f(x)=(a^(2)-b^(2))^(-1//2).cos^(-1)((acosx+b)/(a+bcosx)) a gt b gt 0 and 0 lt x lt pi`, then S.T `f'(x)=(a+bcosx)^(-1)`.

tan^(-1)((a+bcosx)/(b-acosx))

int (dx)/(a+bcosx) = 1/(sqrt(a^(2)-b^(2)) ) cos^(-1) [(b + a cos x)/(a +b cos x)] then int_0^(pi) (dx)/(a+b cosx) =

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

Prove that : 2tan^(-1)(sqrt((a-b)/(a+b))tan""x/2)=cos^(-1)((acosx+b)/(a+bcosx)) .

If y=cos −1 b+acosx/ a+bcosx ​ ,b>a, then dy/dx ​ at x=0, is

If 0 lt x lt pi/2 , show that, cos x gt 1-x^(2)/(2!)