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

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

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

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

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

Solution steps

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

Subtract

1 + 3 cot (x)

from both sides

tan (x) + 3 - 1 - 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

tan (u) - cot (u) = 2

sin (x) sin (x) = 0

15 = arctan (\frac{0.375}{2 x})

cos (θ) (1 + cos (θ)) = sin^{2} (θ)

cos (θ) = - 0.8, sin (π^{2} - θ)

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