Question

已知sin(π/4-x)=5/13,0<x<π/4,求cos2x的值

Answer 1

cos2x=sin(π/2+2x)
=2*sin(π/4+x)*cos(π/4+x)
=2×(5/13)×(12/13)
=120/169

Answer 2

因为0<x<兀/4 所以0<cos(兀/4-x)=根号1-sin(兀/4-x)2=12/13 0<2x<兀/2 sin2(兀/4-x)=cos2x=2sin(兀/4-x)cos(兀/4-x)=2*5/13*12/13=120/169

Answer 3

120/169