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=(3pi)/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{3 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{3 π}{4} + πn

Combine all the solutions

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

0 = a sin (x) + b cos (x)

2 sin^{2} (x) + 9 cos (x) - 6 = 0

tan (θ) = \frac{- 4}{- 3}

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

5 tan^{2} (x) + 5 = 10

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=(3pi)/4+pin