三角函数 例三例四

3:(1) tan(α+β)=2/5,tan(α-β)=1/4
tan2α=tan[(α+β)+(α-β)]
=(2/5+1/4)/(1-2/5x1/4)=13/18
(2):sin(α+β)=-3/5,sin(β-π/4)=12/13,求cos(α+π/4)
cos(α+β)=-4/5,cos(β-π/4)=-5/13
cos(α+π/4)=cos[(α+β)-(β-π/4)]=(-4/5)(-5/13)+(-3/5)(12/13)=-16/65
4:(1)sinα=√15/4 ,cosα=-1/4
sin(α+π/4)/(sin2α+cos2α+1)=(√2/2)(sinα+cosα)/(sinα+cosα)2cosα=√2/4cosα=-√2
(2) cosx-sinx=3√2/5,1-2sinxcosx=18/25 ,2sinxcosx=7/25
(sin2x-2sin^2x)/(1-tanx)=2sinx(cosx-sinx)/[(cosx-sinx)/cosx)]
=2sinxcosx
=7/25