Question

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

Answer 1

你好！

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