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

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

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tan(x)-1= 1/(sqrt(3))-1/(sqrt(3))cot(x)

tan (x) - 1 = \frac{1}{3} - \frac{1}{3} cot (x)

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

Solution steps

tan (x) - 1 = \frac{1}{3} - \frac{1}{3} cot (x)

Subtract

\frac{1}{3} - \frac{1}{3} cot (x)

from both sides

tan (x) - 1 - \frac{1 - cot ( x )}{3} = 0

Simplify

tan (x) - 1 - \frac{1 - cot ( x )}{3} : \frac{3 tan ( x ) - 3 - 1 + cot ( x )}{3}

\frac{3 tan ( x ) - 3 - 1 + cot ( x )}{3} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Rewrite using trig identities

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

Solve by substitution

cot (x) = 3, cot (x) = 1

cot (x) = 3 : x = \frac{π}{6} + πn

cot (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

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

22 cos (x) + 3 = 5

4 tan^{2} (x) + 14 tan (x) + 12 = 0

13 (1 - cos (θ)) = sin^{2} (θ)

8 arcsin (x) = 2 π

2 sin (\frac{1}{2} x) + 1 = 0

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