What is the general solution for sin(x)(2cos(x)-sqrt(3))=0 ?

The general solution for sin(x)(2cos(x)-sqrt(3))=0 is x=2pin,x=pi+2pin,x= pi/6+2pin,x=(11pi)/6+2pin

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sin(x)(2cos(x)-sqrt(3))=0

sin (x) (2 cos (x) - 3) = 0

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

Solution steps

sin (x) (2 cos (x) - 3) = 0

Solving each part separately

sin (x) = 0 or 2 cos (x) - 3 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

2 cos (x) - 3 = 0 : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

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

cos^{2} (x) + 5 cos (x) = cos (x) - 3

- 9 sin (x) - 9 cos (x) = 0

cot (x) = \frac{1}{3}

sin (x) = \frac{5}{2}

2 sin^{2} (θ) + 2 sin (θ) = 0

What is the general solution for sin(x)(2cos(x)-sqrt(3))=0 ?
The general solution for sin(x)(2cos(x)-sqrt(3))=0 is x=2pin,x=pi+2pin,x= pi/6+2pin,x=(11pi)/6+2pin