What is the general solution for (tan(x)-1)(2sin(x)-sqrt(3))=0 ?

The general solution for (tan(x)-1)(2sin(x)-sqrt(3))=0 is x= pi/4+pin,x= pi/3+2pin,x=(2pi)/3+2pin

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(tan(x)-1)(2sin(x)-sqrt(3))=0

(tan (x) - 1) (2 sin (x) - 3) = 0

x = \frac{π}{4} + πn, x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

Solution steps

(tan (x) - 1) (2 sin (x) - 3) = 0

Solving each part separately

tan (x) - 1 = 0 or 2 sin (x) - 3 = 0

tan (x) - 1 = 0 : x = \frac{π}{4} + πn

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

Combine all the solutions

x = \frac{π}{4} + πn, x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

tan (θ) (1 + tan^{2} (θ)) = 0

tan (x) = 9

sin (2 x) = 0, 0 \leq x \leq 2 π

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

- 12 sin^{2} (θ) + 3 = 0

What is the general solution for (tan(x)-1)(2sin(x)-sqrt(3))=0 ?
The general solution for (tan(x)-1)(2sin(x)-sqrt(3))=0 is x= pi/4+pin,x= pi/3+2pin,x=(2pi)/3+2pin