\sin ^{2} \frac{\pi}{8}+\sin ^{2} \frac{3 \pi}{8}+\sin ^{2} \frac{5 \p

1.	\sin ^{2} \frac{\pi}{8}+\sin ^{2} \frac{3 \pi}{8}+\sin ^{2} \frac{5 \pi}{8}+\sin ^{2} \frac{7 \pi}{8}
Answer» sin(π/8) sin(π/8) + sin(3π/8) sin(3π/8) + sin(5π/8) sin(5π/8) + sin(7π/8) sin(7π/8) sin(π/8) = cos(7π/8) sin(3π/8) = cos(5π/8) cos(7π/8) cos(7π/8) + cos(5π/8) cos(5π/8) + sin(5π/8) sin(5π/8) + sin(7π/8) sin(7π/8) = 1 + 1 = 2

\sin ^{2} \frac{\pi}{8}+\sin ^{2} \frac{3 \pi}{8}+\sin ^{2} \frac{5 \pi}{8}+\sin ^{2} \frac{7 \pi}{8}

Answer»

sin(π/8) sin(π/8) + sin(3π/8) sin(3π/8) + sin(5π/8) sin(5π/8) + sin(7π/8) sin(7π/8)

sin(π/8) = cos(7π/8) sin(3π/8) = cos(5π/8)

cos(7π/8) cos(7π/8) + cos(5π/8) cos(5π/8) + sin(5π/8) sin(5π/8) + sin(7π/8) sin(7π/8) = 1 + 1 = 2