Question

已知cos(π/4-α)=12/13,π/4-α是第一象限角，则[sin(π/2 -2α)]/[sin(4/π +α)]的值是

Answer 1

π/4-α是第一象限角
sin(π/4-α)>0
sin²(π/4-α)+cos²(π/4-α)=1
所以 sin(π/4-α)=5/13

原式=sin[2(π/4-α)]/cos[π/2-(π/4+α)]
=2sin(π/4-α)cos(π/4-α)/cos(π/4-α)
=2sin(π/4-α)
=10/13