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=(5pi)/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{5 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{5 π}{6} + πn

cot (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

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

tan^{2} (x) - 3 tan (x) = 0, 0 \leq x \leq 2 π

75 = 50 cosh (\frac{x}{50})

arcsin (\frac{1}{z}) = 0

3 sin^{2} (θ) - 4 = - 4 sin (θ)

2 cos^{2} (x) - 1 + cos (x) = 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=(5pi)/6+pin,x= pi/4+pin