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

The general solution for (cot(x)+1)(sqrt(3)tan(x)-1)=0 is x=(3pi)/4+pin,x= pi/6+pin

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

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

x = \frac{3 π}{4} + πn, x = \frac{π}{6} + πn

Solution steps

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

Solving each part separately

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

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

3 tan (x) - 1 = 0 : x = \frac{π}{6} + πn

Combine all the solutions

x = \frac{3 π}{4} + πn, x = \frac{π}{6} + πn

2 cos^{2} (x) + sin (x) - 1 = 0, 0 \leq x \leq 2 π

cos^{3} (x) = cos^{2} (x)

cos (θ) = - 0.8

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

tan^{2} (x) + 3 tan (x) = - 1

What is the general solution for (cot(x)+1)(sqrt(3)tan(x)-1)=0 ?
The general solution for (cot(x)+1)(sqrt(3)tan(x)-1)=0 is x=(3pi)/4+pin,x= pi/6+pin