Question

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

Answer 1

sin^2(a-60°)+sin^2(a)+sin^2(a+60°)=1.5

证明：把第一个和第三个 打开
(sinacos60-cosasin60)^2+(sinacos60+cosasin60)^2+sin^2(a)
=2(sin^2(a)/4 + 3cos^2(a)/4)+sin^2(a)
=3/2(sin^2(a)+cos^2(a))
=3/2=1.5

Answer 2

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;