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
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