已知cos(4分之派减a )=13分之12,a€(0,4分之派),则sin(4分之派+a)分之cos2a等于?

sin²(π/4-a)+cos²(π/4-a)=1
sin(π/4-a)=5/13
所以cos2a=sin(π/2-2a)
=2sin(π/4-a)cos(π/4-a)
=120/169
sin(π/4+a)
=cos[π/2-(π/4+a)]
=cos(π/4-a)
=12/13
所以原式=10/13