What is the general solution for csc(x)cot(x)+cot(x)=0 ?

The general solution for csc(x)cot(x)+cot(x)=0 is x= pi/2+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

csc(x)cot(x)+cot(x)=0

csc (x) cot (x) + cot (x) = 0

x = \frac{π}{2} + πn

Degrees

x = 9 0^{\circ} + 18 0^{\circ} n

Solution steps

csc (x) cot (x) + cot (x) = 0

Factor

csc (x) cot (x) + cot (x) : cot (x) (csc (x) + 1)

csc (x) cot (x) + cot (x)

Factor out common term

cot (x)

= cot (x) (csc (x) + 1)

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

Solving each part separately

cot (x) = 0 or csc (x) + 1 = 0

cot (x) = 0 : x = \frac{π}{2} + πn

cot (x) = 0

General solutions for

cot (x) = 0

cot (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

csc (x) + 1 = 0 : x = \frac{3 π}{2} + 2 πn

csc (x) + 1 = 0

Move

1

to the right side

csc (x) + 1 = 0

Subtract

1

from both sides

csc (x) + 1 - 1 = 0 - 1

Simplify

csc (x) = - 1

csc (x) = - 1

General solutions for

csc (x) = - 1

csc (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

Merge Overlapping Intervals

x = \frac{π}{2} + πn

tan (x) = \frac{50}{36}

- 2 + cot (x) = - 3

θ, ρ = sin (φ) sin (θ)

3 cos^{2} (x) - 6 cos (x) = - 3, 0 \leq x \leq 2 π

csc (θ) + 2 = 0, 0 \leq θ \leq 2 π

What is the general solution for csc(x)cot(x)+cot(x)=0 ?
The general solution for csc(x)cot(x)+cot(x)=0 is x= pi/2+pin