What is the general solution for (cos(x)-1)(sqrt(3)cot(x)+1)=0 ?

The general solution for (cos(x)-1)(sqrt(3)cot(x)+1)=0 is x=(2pi)/3+pin

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(cos(x)-1)(sqrt(3)cot(x)+1)=0

(cos (x) - 1) (3 cot (x) + 1) = 0

x = \frac{2 π}{3} + πn

Solution steps

(cos (x) - 1) (3 cot (x) + 1) = 0

Solving each part separately

cos (x) - 1 = 0 or 3 cot (x) + 1 = 0

cos (x) - 1 = 0 : x = 2 πn

3 cot (x) + 1 = 0 : x = \frac{2 π}{3} + πn

Combine all the solutions

x = 2 πn, x = \frac{2 π}{3} + πn

Since the equation is undefined for:

2 πn

x = \frac{2 π}{3} + πn

4 cot (x) = 3 csc (x)

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

sin (θ) = \frac{7}{15}

tan^{2} (y) + 3 = 2 sec^{2} (y)

tan (b + 15) \cdot cot (2 b - 5) = 1

What is the general solution for (cos(x)-1)(sqrt(3)cot(x)+1)=0 ?
The general solution for (cos(x)-1)(sqrt(3)cot(x)+1)=0 is x=(2pi)/3+pin