Find the value of `sin(1/4)cos^(-1)((-1)/9)`

1.	Find the value of `sin(1/4)cos^(-1)((-1)/9)`
Answer» Correct Answer - `(1)/(sqrt6)` Let `theta = co^(-1). ((-1)/(9))` `rArr cos theta = (-1)/(9)` `rArr 2 cos^(2). (theta)/(2) = 1 - (1)/(9)` `rArr cos. (theta)/(2) = (2)/(3)` `rArr 1 - 2 sin^(2). (theta)/(4) = (2)/(3)` `rArr 2 sin^(2). (theta)/(4) = (1)/(3)` `rArr sin.(theta)/(4) = (1)/(sqrt6)` (as `(pi)/(2) lt theta lt pi rArr (pi)/(8) lt (theta)/(4) lt (pi)/(4)`) `rArr sin. ((1)/(4) cos^(-1) ((-1)/(9)))) = (1)/(sqrt6)`

Discussion

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