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

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

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

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

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

Solution steps

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

csc (θ) = \frac{7}{3}

6 sin (θ) = 3

2 = sec (x)

2 csc (θ) - 5 = 0

9 cos^{2} (θ) - 10 cos (θ) - 2 = - 7 cos (θ)

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