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= pi/4+pin,x= pi/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{π}{4} + πn, x = \frac{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{π}{4} + πn

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

Combine all the solutions

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

sin (2 θ) + 2 cos (θ) = 0

cot (3 x) = 0, 0 \leq x \leq 2 π

sec (2 x) = 2, 0 \leq x \leq 2 π

sin (x - \frac{π}{4}) = 0

cot (x - \frac{π}{2}) = 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= pi/4+pin,x= pi/3+pin