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=(3pi)/4+pin,x=(5pi)/6+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = \frac{3 π}{4} + πn, x = \frac{5 π}{6} + 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) = - 1, cot (x) = - 3

cot (x) = - 1 : x = \frac{3 π}{4} + πn

cot (x) = - 3 : x = \frac{5 π}{6} + πn

Combine all the solutions

x = \frac{3 π}{4} + πn, x = \frac{5 π}{6} + πn

6 cos^{2} (x) + 7 cos (x) + 2 = 0

sin (θ) = \frac{4}{5}, 0 < θ < \frac{π}{2}, sin (2 θ)

sin (x) - 4 = cos (x) - 4

cos (9 x + 15) = sin (7 x - 5)

3 cos (2 θ) - sin (θ) = 1

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=(3pi)/4+pin,x=(5pi)/6+pin