How do you solve sin(60-x)=2sinx?

Use the trig identity: ##sin (a – b) = sin a.cos b – sin b.cos a##
##sin (60 – x) = sin 60.cos x – cos 60.sin x = (sqr3/2).cos x – (sin x)/2##
(sqr3).cos x – sin x = 4.sin x
##f(x) = (sqr3).cos x – 5sin x = 0.## Divide by cos x –>
##(Condition: cos x not 0 -> x not pi/2 and x not 3pi/2)##
##f(x) = sqr3 – 5tan x -> tan x = (sqr3)/5 = 0.35##
Calculator gives ##x = 19.10 + k.pi##