Find the value of sin2π8 + sin2π4
We know sin2π4 = sin245∘ = (1√2)2 = 12 but, we don't know the value of sin2π8.
Using the formula cos2x = 1 - 2 sin2x
sin2θ = (1−cos2θ2)
sin2π8 = 1−cosπ42 = 1−1√22 = √2−12√2
sin2π8 + sin2π8
= 12 - 12√2 + 12 = 1 - 12√2