已知0<α<π 6sinα+5sin2α=0 求cos(a+π/4)

问题描述:

已知0<α<π 6sinα+5sin2α=0 求cos(a+π/4)

6sinα+5sin2α=0
6sinα+10sinαcosα=0
∵ 0<α<π,
∴ sinα≠0
∴ cosα=-3/5
sinα=4/5
∴ cos(α+π/4)
=cosαcos(π/4)-sinαsin(π/4)
=(-3/5)*(√2/2)-(4/5)*(√2/2)
=-7√2/10