Question

两角和与差的余弦

Answer 1

3cosβ=cos(2α+β)

3cos(α-(α+β))=[cosαcos(α+β)-sinαsin(α+β)]

3[cosαcos(α+β)+sinαsin(α+β)]=[cosαcos(α+β)-sinαsin(α+β)]

4sinαsin(α+β)=-2cosαcos(α+β)

tan(α+β)tanα=-1/2