Question

Diffierentiate: `tan^-1((a + b cos x)/(b - a cos x))` w.r.t.x.

Answer 1

Let y = `tan^-1((a + b cos x)/(b - a cos x))` 

= `tan^-1((a/b + cosx)/(1 - a/b cos x))`

= `tan^-1(a/b) + tan^-1(cosx)`

∴ `dy/dx = 0 + 1/(1 + cos^2x)*d/dxcosx`

= `(-sinx)/(1 + cos^2x)`