What is the general solution for 2cot^4(x)-cot^2(x)-15=0 ?

The general solution for 2cot^4(x)-cot^2(x)-15=0 is x= pi/6+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 >

2cot^4(x)-cot^2(x)-15=0

2 cot^{4} (x) - cot^{2} (x) - 15 = 0

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

Solution steps

2 cot^{4} (x) - cot^{2} (x) - 15 = 0

Solve by substitution

cot (x) = 3, cot (x) = - 3, cot (x) = i \frac{5}{2}, cot (x) = - i \frac{5}{2}

cot (x) = 3 : x = \frac{π}{6} + πn

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

cot (x) = i \frac{5}{2} :

No Solution

cot (x) = - i \frac{5}{2} :

No Solution

Combine all the solutions

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

cos (θ) = \frac{11}{6}

1 + cos (x) = 3 cos (x)

2 cot (θ) + 1 = 0

tan (4 x) + 1 = 0

tan^{2} (x) - 3 = 0, 0 \leq x \leq 2 π

What is the general solution for 2cot^4(x)-cot^2(x)-15=0 ?
The general solution for 2cot^4(x)-cot^2(x)-15=0 is x= pi/6+pin,x=(5pi)/6+pin