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

The general solution for (tan(x)-1)(sqrt(3)tan(x)+1)=0 is x= pi/4+pin,x=(5pi)/6+pin

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

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

x = \frac{π}{4} + πn, x = \frac{5 π}{6} + πn

Solution steps

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

Solving each part separately

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

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

3 tan (x) + 1 = 0 : x = \frac{5 π}{6} + πn

Combine all the solutions

x = \frac{π}{4} + πn, x = \frac{5 π}{6} + πn

sec (2 x) + 1 = 0

sin (θ) = - \frac{4}{7}

6 cos (6 x) = 5

4 sec (x) + 23 = sec (x)

sec (x) sin (x) = 2

What is the general solution for (tan(x)-1)(sqrt(3)tan(x)+1)=0 ?
The general solution for (tan(x)-1)(sqrt(3)tan(x)+1)=0 is x= pi/4+pin,x=(5pi)/6+pin