Evaluate each of the following: `sin(sec^(-1)(17)/8)` (ii) `"c o s e c"(cos^(-1)3/5)` (iii) `sec(sin^(-1)(12)/(13))`

Explanation

(i) `\sin (\sec ^{-1} \frac{17}{8})=\sin (\cos ^{-1} \frac{8}{17})`

`=\sin [\sin ^{-1} \sqrt{1-(\frac{8}{17})^{2}}] \quad[\because \cos ^{-1} x=\sin ^{-1} \sqrt{1-x^{2}}]`

`=\sin [\sin ^{-1}(\sqrt{1-\frac{64}{289}})]`

`=\sin [\sin ^{-1}(\sqrt{\frac{225}{289}})]`

`=\sin [\sin ^{-1} \frac{15}{17}]`

`=\frac{15}{17}`


(ii)

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