若tanα=a,则sin(-5π-α）×cos(3π+α)=?求具体解题步骤 特别是化简的部分 谢谢

Question

若tanα=a,则sin(-5π-α）×cos(3π+α)=?
求具体解题步骤 特别是化简的部分 谢谢

Answer 1

sin(-5π-α）×cos(3π+α)
=sin(6π-5π-α)×cos(2π+π+α)
=sin(π-α)×cos(π+α)
=sinα×(-cosα)
=-sinαcosα
=-1/2*sin2α
=-1/2*(2tanα)/[1+(tanα)^2]
=-1/2*(2*a)/[1+a^2]
=-a/(1+a^2)