∵cos（π/4+x）=4/5,∴cosx-sinx=(4/5)√2两边平方得,cos²x+sin²x-2sinxcosx=32/25则,2sinxcosx=-7/25∴（cosx+sinx)²=1+2sinxcosx=18/25∵x∈（-π/2,-π/4）∴cosx+sinx=（-3/5)√2解得sinx=（-7/...