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

1 Answer
May 3, 2015

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