tan[π/4+a]×cos 2a /2cos ²[π/4-a]
=tan(π/4+a)*sin(π/2+2a)/[2cos²(π/2-(π/4+a)]
=tan(π/4+a)*sin(π/2+2a)/[2sin²(π/4+a)]
∵ π/2+2a=2*(π/4+a)
=[sin(π/4+a)/cos(π/4+a)]*2sin(π/4+a)*cos(π/4+a)/[2sin²(π/4+a)]
=[2sin²(π/4+a)]/[2sin²(π/4+a)]
=1
tan[π/4+a]×cos 2a /2cos ²[π/4-a]
=tan(π/4+a)*sin(π/2+2a)/[2cos²(π/2-(π/4+a)]
=tan(π/4+a)*sin(π/2+2a)/[2sin²(π/4+a)]
∵ π/2+2a=2*(π/4+a)
=[sin(π/4+a)/cos(π/4+a)]*2sin(π/4+a)*cos(π/4+a)/[2sin²(π/4+a)]
=[2sin²(π/4+a)]/[2sin²(π/4+a)]
=1