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Question
Evaluate: sin`[1/2 cos^-1 (4/5)]`
Solution
Let `cos^-1 (4/5)` = A
Then `4/5` = cos A
cos A = `4/5`
∴ `sin [1/2 cos^-1 (4/5)] = sin (1/2 "A") = sin "A"/2`
We know that
cos A = 1 - 2 sin2 `"A"/2`
`4/5 = 1 - 2 sin^2 "A"/2`
`2 sin^2 "A"/2 = 1 - 4/5`
`2 sin^2 "A"/2 = 1/5`
∴ `sin^2 "A"/2 = 1/10`
∴ `sin "A"/2 = 1/sqrt10`
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