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Prove that\sin ^{2} \pi / 8+\sin ^{2} 3 \pi / 8+\sin ^{2} 5 \pi / 8+\sin ^{2} 7 \pi / 8=2

Answer»

Sin²π/8+sin²3π/8+sin²5π/8+sin²7π/8=sin²π/8+sin²3π/8+sin²(π/2+π/8)+sin²(π/2+3π/8)=sin²π/8+sin²3π/8+cos²π/8+cos²3π/8=(sin²π/8+cos²π/8)+(sin²3π/8+cos²3π/8) [∵, sin²Ф+cos²Ф=1]=1+1=2



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