Question

已知sin(π/4--x)=5/13,0<x<π/4,求sin2x/cos(π/4--x)的值

速度 急求啊

Answer 1

sin(π/4-x)=5/13
0＜x＜π/4
0＜π/4-x
cos(π/4-x)=12/13
sin(π/4-x)
=sinπ/4cosx-cosπ/4sinx
=√2/2cosx-√2/2sinx
=√2/2(cosx-sinx)=5/13
两边平方
1/2(cosx-sinx)^2=25/169
1-2sinxcosx=50/169
sin2x=119/169
sin2x/cos(π/4-x)
=(119/169)/(12/13)
=119/156