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

题目

已知sin(π/4-x)=5/13,0＜x＜π/4,求sin2x/cos(π/4-x)的值
要用到二倍角公式..还不熟练TAT

答案

数学之美团为你解答
sin(π/4 - x) = 5/13
0 < x < π/4
0 < π/4 - x < π/4
cos(π/4 - x) > 0
∴cos(π/4 -x) = 12/13
sin(2x)
= cos(π/2 - 2x)
= cos 2(π/4 -x)
= 2cos²(π/4 -x) - 1
sin(2x) / cos(π/4 - x)
= 2cos(π/4 -x) －1/cos(π/4 - x)
= 2×12/13 - 13/12
= 119/156