已知α是第二象限的角,且cos(α-π/2)=1/5,求(sin(π+α)cos(π-α)tan(-3π/2-α))/(tan(π/2+α)cos(3π/2+α))的值
问题描述:
已知α是第二象限的角,且cos(α-π/2)=1/5,求(sin(π+α)cos(π-α)tan(-3π/2-α))/(tan(π/2+α)cos(3π/2+α))的值
答
cos(a-π/2)=1/5
sina=1/5
α是第二象限的角
cosa=-2√6/5
(sin(π+a)cos(π-a)tan(-3π/2-a))/(tan(π/2+a)cos(3π/2+a))
=-sina(-cosa)tana/((-tana)sina)
=-cosa
=2√6/5