`tan^(-1)(tan theta)={(pi+theta,-(3pi)/2lt theta lt -(pi)/2),(theta , -(pi)/2 lt theta lt (pi)/2),(-pi+theta,(pi)/2lt thetalt (3pi)/2):} sin^(-1)(sin theta)= {(-pi-theta,(3pi)/2le theta lt -(pi)/2),(theta, -(pi)/2le theta le (pi)/2),(pi-theta,(pi)/2lt theta le (3pi)/2):}`
`cos^(-1)(cos theta)={(-theta, -pi le theta lt 0),(theta, 0 le theta le pi),(2pi-theta,pilt theta le 2pi):}`
Based onthe above results, prove each of the following:
(i) `cos^(-1)x=sin^(-1)sqrt(1-x^(2))` if `0ltxlt1`
(ii) `sin^(-1)x=cos^(-1)sqrt(1-x^(2))` if `0ltxlt1`
(iii) `cos^(-1)x=pi+"tan"^(-1)(sqrt(1-x^(2)))/x` if `-1ltxlt0`

Explanation

NA