已知三角形ABC中,tanA=-5/12.则sin(5π/2-A)乘cos(3π/2+A)等于.

问题描述:

已知三角形ABC中,tanA=-5/12.则sin(5π/2-A)乘cos(3π/2+A)等于.

∵tanA=-5/12
∴sin(5π/2-A)*cos(3π/2+A)
=sin(2π+π/2-A)*cos(π+π/2+A)
=cosAsinA/1
=cosAsinA/(sin²A+cos²A)
=tanA/(tan²A+1)
=-60/169