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

The general solution for tan(x)-1=-sqrt(3)+sqrt(3)cot(x) is x=(2pi)/3+pin,x= pi/4+pin

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

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

x = \frac{2 π}{3} + πn, x = \frac{π}{4} + πn

Solution steps

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

Subtract

- 3 + 3 cot (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

cot (x) = - \frac{3}{3} : x = \frac{2 π}{3} + πn

cot (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

x = \frac{2 π}{3} + πn, x = \frac{π}{4} + πn

14 cos^{2} (x) = 7

cos (2 θ) + sin (2 θ) = - 1

sin (θ) = \frac{19}{27}

sin^{4} (x) = \frac{1}{2} cos^{2} (x)

3 cos^{2} (x) + cos (x) - 2 = 0

What is the general solution for tan(x)-1=-sqrt(3)+sqrt(3)cot(x) ?
The general solution for tan(x)-1=-sqrt(3)+sqrt(3)cot(x) is x=(2pi)/3+pin,x= pi/4+pin