已知sin^2(30°)+sin^2(90°)+sin^2(150°)=1.5
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已知sin^2(30°)+sin^2(90°)+sin^2(150°)=1.5
sin^2(5°)+sin^2(65°)+sin^2(125°)=1.5 观察两等式 写出一般性命题 并给出证明
sin^2(5°)+sin^2(65°)+sin^2(125°)=1.5 观察两等式 写出一般性命题 并给出证明
![已知sin^2(30°)+sin^2(90°)+sin^2(150°)=1.5](/uploads/image/z/18936709-61-9.jpg?t=%E5%B7%B2%E7%9F%A5sin%5E2%2830%C2%B0%29%2Bsin%5E2%2890%C2%B0%29%2Bsin%5E2%28150%C2%B0%29%3D1.5)
sin^2(t-60)+sin^2(t)+sin^2(t+60)=1.5;
sin^2(t-60)+sin^2(t)+sin^2(t+60)
=(sintcos60-costsin60)^2+(sintcos60+costsin60)^2+sin^2(t)
=2(sintcos60)^2+2(costsin60)^2+sin^2(t)
=3/2((sint)^2+(cost)^2)
=3/2;
sin^2(t-60)+sin^2(t)+sin^2(t+60)
=(sintcos60-costsin60)^2+(sintcos60+costsin60)^2+sin^2(t)
=2(sintcos60)^2+2(costsin60)^2+sin^2(t)
=3/2((sint)^2+(cost)^2)
=3/2;
已知sin平方30度+sin平方90度+sin平方150度=3/2,sin平方5度+sin平方65度+sin平方125度
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