(i) The principal value of cos^-1 (-1/2) (iii) Express tan ^1 (cos x /1-sinx) in the simplest form

Question

(i) The principal value of cos ^-1\((\frac{-1}{2})\)

(ii) Express tan^-1 \(\frac{cos x} {1-sin x}\) in the simplest form

Answer 1

(i) cos^-1 \(-\frac{1}{2}\) = π - cos\(\frac{1}{2}\) = π - \(\frac{π}{3}\) = \(\frac{2π}{3}\)

(ii) LHS = tan^-1 (\(\frac{cosx}{1-sinx}\))