Question

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

Answer 1

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`