Question

Find all the angles between 0 and 2π that satisfy the following equation:

cos(x-0.4)=3sinx

I can't seem to simplify it correctly ><
Help is greatly appreciated.

Answer 1

\[\cos x \cos .4 + \sin x \sin .4 = 3 \sin x\]
\[\cos x \cos .4 = 3 \sin x - \sin x \sin .4\]
\[\cos x \cos .4 = \sin x (3 - \sin .4)\]
\[\cos .4 = \frac{\sin x}{\cos x} (3 - \sin .4)\]
\[\tan x = \frac{\cos .4}{3 - \sin .4}\]

Answer 2

aah thank you

Answer 3

yw :)