What is the general solution for sin(x+pi/6)+sin(x-pi/6)=-(sqrt(3))/2 ?

The general solution for sin(x+pi/6)+sin(x-pi/6)=-(sqrt(3))/2 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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sin(x+pi/6)+sin(x-pi/6)=-(sqrt(3))/2

sin (x + \frac{π}{6}) + sin (x - \frac{π}{6}) = - \frac{3}{2}

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

sin (x + \frac{π}{6}) + sin (x - \frac{π}{6}) = - \frac{3}{2}

Rewrite using trig identities

3 sin (x) = - \frac{3}{2}

Divide both sides by

3

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

General solutions for

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

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

3 csc (\frac{2 x}{3}) - 2 = 0

cos (θ) = \frac{8}{10}

5 sin (a) + 3 = sin (a) + 2

csc (3 x) = 2

sin (x) = 0, 6

What is the general solution for sin(x+pi/6)+sin(x-pi/6)=-(sqrt(3))/2 ?
The general solution for sin(x+pi/6)+sin(x-pi/6)=-(sqrt(3))/2 is x=(7pi)/6+2pin,x=(11pi)/6+2pin