若tanα=a 则sin(-5π-α）×cos(3π+α)=?求具体解

查题易2023-04-05 18:22:58 数学已帮助人

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

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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)