Question

若α,β属于(0,二分之派)且cosα=0.6,cos(α+β)=-5/13,求cos（2α+β）和cos2β的值

Answer 1

α,β属于(0,二分之派),所以sinα>0且sin(α+β)>0,sinα=根号(1-cos^2α)=0.8,sin(α+β)=12/13

cos(2α+β)=cosαcos(α+β)-sinαsin(α+β)=3/5*(-5/13)-4/5*12/13=-63/65

cosβ=cos(α+β)cosα+sin(α+β)sinα=3/5*(-5/13)+4/5*12/13=33/65

cos2β=2cos^2β-1=2*1089/4225-1=2047/4225