Find the function value and simplify

Question

sin² (7∏ / 8 )

Answer 1

sin²(7π/8) = (1 - cos7π/4)/2 = (1 - cosπ/4)/2 = (2 - √2)/4

Answer 2

Use the half-angle formula sin(θ/2) = √[(1 – cos θ)/2]

So sin(7π/8) = √[(1 – cos(7π/4))/2]

Square both sides to get

sin²(7π/8) = (1 – cos(7π/4))/2 = (1 – √2/2)/2 = (2 – √2)/4

Answer

sin²(7π/8) = (2 – √2)/4