What is the general solution for sin(x+pi/6)-sin(x-pi/6)= 1/2 ?

The general solution for sin(x+pi/6)-sin(x-pi/6)= 1/2 is x= pi/3+2pin,x=(5pi)/3+2pin

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

sin (x + \frac{π}{6}) - sin (x - \frac{π}{6}) = \frac{1}{2}

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

sin (x + \frac{π}{6}) - sin (x - \frac{π}{6}) = \frac{1}{2}

Rewrite using trig identities

cos (x) = \frac{1}{2}

General solutions for

cos (x) = \frac{1}{2}

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

tan (θ) = \frac{5}{12}

cos (3 x) = \frac{3}{2}

sin (x) = cos (x) - 1

2 sin (x) cos (x) = cos (x)

tan^{2} (θ) - 1 = 0

What is the general solution for sin(x+pi/6)-sin(x-pi/6)= 1/2 ?
The general solution for sin(x+pi/6)-sin(x-pi/6)= 1/2 is x= pi/3+2pin,x=(5pi)/3+2pin