Question

cos（α+β）*cos（α-β）=1/5,求cos^2(α)-sin^2(β)

Answer 1

解：cos（α+β）*cos（α-β）=(cosαcosβ-sinαsinβ)*(cosαcosβ+sinαsinβ)
=cos^2(α)cos^2(β) -sin^2(α)sin^2(β)
= cos^2(α)(1-sin^2(β) )-(1- cos^2(α)) sin2β
= cos^2(α)- cos^2(α)sin^2(β) - sin^2(β) + cos^2(α)sin^2(β)
=1/5
希望楼主满意

Answer 2

由cos（α+β）*cos（α-β）=1/5得：cos^2(α)+cos^2(β)=6/5
∴ cos^2(α)-sin^2(β) =6/5-cos^2(β)-sin^2(β)=6/5-（cos^2(β)+sin^2(β)）=6/5-1=1/5