Question

已知α、β均为锐角 且cosα=1/5 cos(α+β)=(√2-4√3)/10 求β

Answer 1

cosα=1/5,所以sinα=2√6/5,cos(α+β)=(√2-4√3)/10,所以sin（α+β）=(√2+4√3)/10

cosβ=cos(α+β-α)=cos(α+β)cosα+sin（α+β）sinα

=(√2-4√3)/10×1/5＋(√2+4√3)/10×2√6/5

=√2/2

所以β=45度