已知sin(兀/4+x)=-3/5,则sin2x的值为?
问题描述：
已知sin(兀/4+x)=-3/5,则sin2x的值为?
答
sin(π/4+x)=-3/5 sinxcosπ/4+cosxsinπ/4=-3/5 √2/2(sinx+cosx)=-3/5 sinx+cosx = -3√2/5 (sinx+cosx)^2 = (-3√2/5)^2 sin^2x+cos^2x+2sinxcosx=18/25 1+sin2x=18/25 sin2x = -7/25
答
sin(π/4+x)=-3/5
sinxcosπ/4+cosxsinπ/4=-3/5
√2/2(sinx+cosx)=-3/5
sinx+cosx = -3√2/5
(sinx+cosx)^2 = (-3√2/5)^2
sin^2x+cos^2x+2sinxcosx=18/25
1+sin2x=18/25
sin2x = -7/25