Question

Find the value of :

`sin  pi/8`

Answer 1

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`