Trigonometric Identities and equations

[wei1006]

1) Problem statement:
Solve the trigonometric equation for the domain is. 0°<x<360°
5(sinx - cosx) = 4sinx - 3cosx

2) relevant equations:
secx=1/cosx
cosec x=1/sinx
cot x= 1/tanx
tan x=sinx/cosx
cot x=cosx/sinx
sin^2 x + cos^2 x=1
1 + tan^2 x= sec^2 x
1+ cot^2 x = cosec^2 x

Template of answer:
New domain:
Basic angle=
Quadrants=
Solve for x
3)Attempt the question
5(sin x - cosx)=4sinx - 3cosx
5sinx-4sinx-5cosx+3cosx=0
sinx - 2 cos x=0

 

[Orodruin]

sinx - 2 cos x=0

Fine up to here, so what is the solution to this equation?

 

[wei1006]

I am not sure how to continue...

 

[Orodruin]

How about trying to rewrite it by placing the 2 cos x on the other side and then dividing by something that makes it easier?

 

[wei1006]

Thank you for your help, have solved it