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

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

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

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

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

Solution steps

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

Solving each part separately

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

cot (x) + 1 = 0 : x = \frac{3 π}{4} + πn

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

Combine all the solutions

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

3 sin (θ) = - cos (θ)

- 2 sin (x) + 1 = 0

sin (2 θ) = - \frac{3}{2}, 0 \leq θ \leq 2 π

2 - 2 cos^{2} (\frac{x}{2}) = 2 sin^{2} (x)

3 tanh^{2} (x) = 5 sech (x) + 1

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