Question

Use a half-angle identity to find the exact value of sinPi/8

Answer 1

Explanation:

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look this solution :

Answer 2

sin(π/8) = (1/2)√(2-√2)

Explanation:

Using the half-angle formula ...

`\sin{(\theta)/(2)}=\sqrt{(1-cos(\theta))/(2)}`

We can let θ = π/4 and simplify the result as follows:

`\sin{(\pi)/(8)}=\sqrt{(1-cos((\pi/4)))/(2)}=\sqrt{(1-(√(2))/(2))/(2)}=\sqrt{(2-√(2))/(4)}\\\\=\boxed{(1)/(2)\sqrt{2-√(2)}}}`