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प्रश्न
Find the value of :
`cos pi/8`
उत्तर
We know that, cos2θ = 2cos2θ − 1
1 + cos2θ = 2cos2θ
cos2θ = `(1 + cos2theta)/2`
Substituting θ = `pi/8`, we get
`cos^2 pi/8 = (1 + cos 2(pi/8))/2`
= `(1 + cos (pi/4))/2`
= `(1 + 1/sqrt(2))/2`
= `(sqrt(2) + 1)/(2sqrt(2)`
∴ `cos pi/8 = sqrt((sqrt(2) + 1)/(2sqrt(2))) ...[because cos pi/8 "is posiive"]`
∴ `cos pi/8 = sqrt((sqrt(2) + 1)/(2sqrt(2)) xx sqrt(2)/sqrt(2)`
= `sqrt((2 + sqrt(2))/4`
∴ `cos pi/8 = sqrt(2 + sqrt(2))/2`
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Find the value of :
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