设sinθ+cosθ=1/2 求sin2θ
问题描述：
设sinθ+cosθ=1/2 求sin2θ
答
已知：sinθ + cosθ = 1/2
则：(sinθ + cosθ)^2 = (sinθ)^2 + (cosθ)^2 + 2sinθcosθ =[(sinθ)^2 + (cosθ)^2] + 2sinθcosθ
= 1 + 2sinθcosθ
= 1 + sin(2θ)
= 1/4
即：sin(2θ) = 1/4 - 1 = -3/4