Question

哪位数学大能能帮我看看这道题，谢谢

Answer 1

sin(π/4 -x) = 3/5
(√2/2)(cosx - sinx) = 3/5
cosx - sinx =3√2/5
1-tanx =(3√2/5)secx
25(1-tanx)^2 = 18(secx)^2
7(tanx)^2 -50tanx +7=0
(tanx-7)(7tanx-1) = 0
tanx =1/7
tan(2x+π/4)

=(1+ tan2x)/(1-tan2x)
={ 1+ 2tanx/[1-(tanx)^2 ] }/ { 1-2tanx/[1-(tanx)^2 ] }
= [ 1-(tanx)^2 + 2tanx ]/[ 1-(tanx)^2 -2tanx]
=( 1- 1/49 + 2/7) /( 1- 1/49 - 2/7)
=(49-1+14)/(49-1-14)
=62/34
=31/17