Question

Convert (i) `tan^(-1)3,` (ii) `sin^(-1)(-1//3)` in terms of cosine inverse.

Answer 1

(i) Let `theta=tan^(-1)3impliestantheta=3impliescostheta=1/(sqrt(10))impliestheta=cos^(-1)1/(sqrt(10))`
(ii) `sin^(-1)(-1//3)=-sin^(-1)(1//3)`
Let `theta=sin^(-1)(1//3)impliessintheta=1/3impliescostheta=(2sqrt(2))/3impliestheta=cos^(-1)(2sqrt(2))/3`
`implies sin^(-1)(-1//3)=-cos^(-1)(2sqrt(2))/3`