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

π/4-α是第一象限角sin(π/4-α)>0sin²(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...