solve trig problem?

Question

sin(x+pi/6)-sin(x-pi/6)=1/2

Answer 1

LHS
sin x cos π/6 + cos x sin π/6
sin x cos π/6 - cos x sin π/6
Subtracting gives:-
2 cos x sin π/6 = cos x

cos x = 1/2
x = π/3 , 5π/3

Answer 2

using factor formula,
sin(x+pi/6)-sin(x-pi/6)=1/2
2cos x sin(pi/3)=1/2
(2cos x)(3^(1/2))/2=1/2
2cos x=1/(3^(1/2))
cos x=1/(2)(3^(1/2))
x=73.22,286.88 in degrees and x is in the interval [0,360].

Answer 3

sin(x+pi/6)-sin(x-pi/6)=1/2
[sinx cos(pi/6) + sin(pi/6)cosx] - [sinx cos(pi/6) - sin(pi/6)cosx]=1/2

sinx cos(pi/6) + sin(pi/6)cosx - sinx cos(pi/6) + sin(pi/6)cosx =1/2

2 . sin(pi/6)cosx =1/2
2 * 0.5 cosx =1/2
cosx =1/2
x = pi/3 . . . or . . . x = (5/3) pi

Alejandra

Answer 4

sin(x + (pi/6)) = sin(x)cos(pi/6) + sin(pi/6)cos(x)
sin(x - (pi/6)) = sin(x)cos(pi/6) - sin(pi/6)cos(x)

sin(x + (pi/6)) - sin(x - (pi/6)) =

(sin(x)cos(pi/6) + sin(pi/6)cos(x)) - (sin(x)cos(pi/6) - sin(pi/6)cos(x))

sin(x)cos(pi/6) + sin(pi/6)cos(x) - sin(x)cos(pi/6) + sin(pi/6)cos(x)

sin(pi/6)cos(x) + sin(pi/6)cos(x)

2(sin(pi/6)cos(x))
2((1/2)cos(x))
cos(x)

so

cos(x) = (1/2)
x = pi/3 and 5pi/3