[" 23."2tan^(-1)(sqrt((a-b)/(a+b))tan(x)/(2))=],[[" (a) "cos^(-1)((b+a cos x)/(a+b cos x))," (b) "cos^(-1)((b+a cos x)/(a-b cos x))],[" (c) "cos^(-1)((b-a cos x)/(a+b cos x))," (d) "cos^(-1)((b-a cos x)/(a-b cos x))]]

2 tan ^(-1) (sqrt((a-b)/(a+b))tan""(x)/(2))=cos^(-1)""(acos x+b)/(a+b cos x)

d/dx ((a-b cos x)/(a+b cos x)) =

2tan^(-1)[sqrt((a-b)/(a+b))tan ""theta/2]= a) cos^(-1)((a cos theta + b)/(a+bcos theta)) b) cos^(-1)((a+b cos theta)/(acos theta+b)) c) cos^(-1)((acos theta)/(a+bcos theta)) d) cos^(-1)((bcos theta)/(acos theta+b))

The value 2tan^(-1)[sqrt((a-b)/(a+b))(tan theta)/(2)] is equal to cos^(-1)((a cos theta+b)/(a+b cos theta))(b)cos^(-1)((a+b cos theta)/(a cos theta+b))cos^(-1)((a cos theta)/(a+b cos theta)) (d) cos^(-1)((b cos theta)/(a cos theta+b))

{Tan ^(-1) ((a + bcos x )/( b + a cos x ))}=

(d)/(dx ) {Cos^(-1) ((a+b cos x )/(a cos x +b)) (a lt b )=

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))

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