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##