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प्रश्न
Find the value of :
`sin pi/8`
उत्तर
We know that sin2 θ = `(1 - cos 2θ)/2`
Substituting θ = `pi/8`, we get
`sin^2 pi/8 = (1 - cos pi/4)/2`
= `(1 - 1/sqrt2)/2`
= `(sqrt2 - 1)/(2sqrt2)`
∴ `sin pi/8 = sqrt((sqrt(2) - 1)/(2sqrt(2)))` ....`[∵ sin pi/8 "is positive"]`
∴ `sin pi/8 = sqrt((sqrt(2) - 1)/(2sqrt(2)) xx sqrt(2)/sqrt(2)`
= `sqrt((2 - sqrt2)/4)`
∴ `sin pi/8 = sqrt(2 - sqrt2)/2`
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