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

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

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sin(x)(tan(x)-sqrt(3))=0

sin (x) (tan (x) - 3) = 0

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

Solution steps

sin (x) (tan (x) - 3) = 0

Solving each part separately

sin (x) = 0 or tan (x) - 3 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

tan (x) - 3 = 0 : x = \frac{π}{3} + πn

Combine all the solutions

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

sin (x) \cdot cos (x) = 2 cos^{2} (x)

cos (θ) tan (θ) + cot (θ) = csc (θ)

tan^{2} (x) = \frac{1}{cot ( x )}

\frac{sin ( θ )}{cos ( θ )} = 3

48 sin^{2} (x) = 48 - 24 cos (x)

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