Question

若tan阿尔法=a,则sin(-5π-阿尔法)cos(3π+阿尔法）=?

Answer 1

tanα=asinα=a/(1+a^2)^0.5cosα=1/(1+a^2)^0.5sin(-5π-α)*cos(3π+α)=sin(6π-5π-α)*cos(3π+α-2π)=sin(π-α)*cos(π+α)=sinα*(-cosα)=-(a/(1+a^2)^0.5)*(1/(1+a^2)^0.5)=-a/(1+a^2)