Question

Find the value of:

`cos  pi/8`

Answer 1

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`