Bila 2 cos (x+ 1/4 pi)= cos(x-1/4 pi) maka tentukan nilai tan 2 x

2 cos(x+45°)=cos(x-45°)
2(cosx.cos45-sinx.sin45)=(cosx.cos45+sinx.sin45)
2(cosx.1/2√2-sinx.1/2√2)=(cosx.1/2√2+sinx.1/2√2)
2(1/2√2(cosx-sinx)=1/2√2(cosx+sinx)
2(cosx-sinx)=cosx+sinx.....(1)
→).Perbandingan sinx dan cosx
2cosx-2sinx=cosx+sinx
2cosx-cosx=sinx+2sinx
cosx=3sinx
Jadi cos:sin = 1:3
→).Menentukan nilai sinx dan cosx
(cosx+sinx/cosx-sinx)²=2²
cos²x+sin²x+2sinxcosx/cos²x-sin²x-2sinxcosx=4
1+sin2x/1-sin2x=4
1+sin2x=4-4sin2x
5sin2x=3
sin2x=3/5
2sinx.cosx=3/5
sinx.cos.x=3/10
[sin:cos = 3:1]
(3/√10)×(1/√10)=3/10
sinx=3/√10
cosx=1/√10
tanx=3/1 = 3
tan2x=2tanx/1-tan²x
tan2x=2(3)/1-(3)²
tan2x=6/1-9
tan2x=6/-8
tan2x=-3/4