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Question
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
Solution
`cos (pi/4 + theta/2)`, when sin θ = `8/9`
`cos (pi/4 + theta/2) = sqrt((1 + cos2 (pi/4 + theta/2))/2`
= `sqrt((1 + cos (pi/2 + theta))/2`
= `sqrt((1 - sin theta)/2`
= `sqrt((1 - 8/9)/2`
= `sqrt((9 - 8)/18`
= `sqrt(1/18)`
= `sqrt(1/(9 xx 2))`
= `1/(3sqrt(2))`
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