化简sin(π+α)cos(3π/2+α)+sin(π/2+α)cos(π+α)

问题描述:

化简sin(π+α)cos(3π/2+α)+sin(π/2+α)cos(π+α)
答案是-1 求过程

根据第一、二象限sin值取正,第一、四象限cos值取正,sin(π+α)cos(3π/2+α)+sin(π/2+α)cos(π+α)=-sinacosa+sina(-cosa)=-2sinacosa=-sin2a,若a=π/4,则-sin2a=-sinπ/2=-1