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Question
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
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Solution
`sin (pi/4 - theta/2)`, when sin θ = `1/25`
`sin (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 - 1/25)/2`
= `sqrt((25 - 1)/50`
= `sqrt(24/50)`
= `sqrt(12/25)`
= `sqrt((4 xx 3)/(5 xx 5)`
= `(2sqrt(3))/5`
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