What is the general solution for cot^3(x)+2cot^2(x)-3cot(x)-6=0 ?

The general solution for cot^3(x)+2cot^2(x)-3cot(x)-6=0 is x=2.67794…+pin,x=(5pi)/6+pin,x= pi/6+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cot^3(x)+2cot^2(x)-3cot(x)-6=0

cot^{3} (x) + 2 cot^{2} (x) - 3 cot (x) - 6 = 0

x = 2.67794 \dots + πn, x = \frac{5 π}{6} + πn, x = \frac{π}{6} + πn

Solution steps

cot^{3} (x) + 2 cot^{2} (x) - 3 cot (x) - 6 = 0

Solve by substitution

cot (x) = - 2, cot (x) = - 3, cot (x) = 3

cot (x) = - 2 : x = arccot (- 2) + πn

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

cot (x) = 3 : x = \frac{π}{6} + πn

Combine all the solutions

x = arccot (- 2) + πn, x = \frac{5 π}{6} + πn, x = \frac{π}{6} + πn

Show solutions in decimal form

x = 2.67794 \dots + πn, x = \frac{5 π}{6} + πn, x = \frac{π}{6} + πn

sin^{2} (x) = cos^{3} (x)

12 cot^{2} (x) - cot (x) = 1

2 + cos (x) = 3 \frac{cos ^{2} ( x )}{2} + \frac{sin ^{2} ( x )}{2}

sin^{2} (x) + sin^{6} (x) = 3 cos^{2} (2 x)

cot^{2} (x) - 7 cot (x) + 10 = 0

What is the general solution for cot^3(x)+2cot^2(x)-3cot(x)-6=0 ?
The general solution for cot^3(x)+2cot^2(x)-3cot(x)-6=0 is x=2.67794…+pin,x=(5pi)/6+pin,x= pi/6+pin