Question

已知x+y=派/4,求(1+tanx)(1+tany) 已知sin(派/4+x）*sin(派/4-x）=1/6,且x属于

Answer 1

x+y=π/4,

tanx+tany=1-tanxtany,

(1+tanx)(1+tany)

=1+(tanx+tany)+tanxtany

=2.

积化和差公式

sin(π/4+x）*sin(π/4-x）

=－1/2[cos π/2-cos2x]

=1/6.

cos2x=1/3>0,

又x∈（－2π,π）,