What is the general solution for cot^2(x)+2cot(x)+1=0 ?

The general solution for cot^2(x)+2cot(x)+1=0 is x=(3pi)/4+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cot^2(x)+2cot(x)+1=0

cot^{2} (x) + 2 cot (x) + 1 = 0

x = \frac{3 π}{4} + πn

Solution steps

cot^{2} (x) + 2 cot (x) + 1 = 0

Solve by substitution

cot (x) = - 1

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

Combine all the solutions

x = \frac{3 π}{4} + πn

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

3 sin (θ) = - cos (θ)

- 2 sin (x) + 1 = 0

sin (2 θ) = - \frac{3}{2}, 0 \leq θ \leq 2 π

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

What is the general solution for cot^2(x)+2cot(x)+1=0 ?
The general solution for cot^2(x)+2cot(x)+1=0 is x=(3pi)/4+pin