What is the general solution for cot(x)+csc(x)cos(x)=2,cot(x) ?

The general solution for cot(x)+csc(x)cos(x)=2,cot(x) is No Solution for x\in\mathbb{R}

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Popular >

cot(x)+csc(x)cos(x)=2,cot(x)

Solution

cot (x) + csc (x) cos (x) = 2, cot (x)

Solution

No Solution for x \in R

Solution steps

cot (x) + csc (x) cos (x) = 2, cot (x)

Subtract

2

from both sides

cot (x) + csc (x) cos (x) - 2 = 0

Rewrite using trig identities

- 2 + cot (x) + cos (x) csc (x)

csc (x) cos (x) = cot (x)

csc (x) cos (x)

Express with sin, cos

csc (x) cos (x)

Use the basic trigonometric identity:

csc (x) = \frac{1}{sin ( x )}

= \frac{1}{sin ( x )} cos (x)

Simplify

\frac{1}{sin ( x )} cos (x) : \frac{cos ( x )}{sin ( x )}

\frac{1}{sin ( x )} cos (x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 cos ( x )}{sin ( x )}

Multiply:

1 \cdot cos (x) = cos (x)

= \frac{cos ( x )}{sin ( x )}

= \frac{cos ( x )}{sin ( x )}

= \frac{cos ( x )}{sin ( x )}

Use the basic trigonometric identity:

\frac{cos ( x )}{sin ( x )} = cot (x)

= cot (x)

= - 2 + cot (x) + cot (x)

Simplify

= - 2 + 2 cot (x)

- 2 + 2 cot (x) = 0

Move

2

to the right side

- 2 + 2 cot (x) = 0

Add

2

to both sides

- 2 + 2 cot (x) + 2 = 0 + 2

Simplify

2 cot (x) = 2

2 cot (x) = 2

Divide both sides by

2

2 cot (x) = 2

Divide both sides by

2

\frac{2 cot ( x )}{2} = \frac{2}{2}

Simplify

cot (x) = 1

cot (x) = 1

General solutions for

cot (x) = 1

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}{4} + πn

x = \frac{π}{4} + πn

Solutions for the range

cot (x)

No Solution for x \in R

Popular Examples

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960 = 480 (1 - cos (7.5 x))

8=8tan(θ)

8 = 8 tan (θ)

2sin(2x)-3cos(x)=0

2 sin (2 x) - 3 cos (x) = 0

4cos(θ)=2cos(θ)

4 cos (θ) = 2 cos (θ)

Frequently Asked Questions (FAQ)

What is the general solution for cot(x)+csc(x)cos(x)=2,cot(x) ?
The general solution for cot(x)+csc(x)cos(x)=2,cot(x) is No Solution for x\in\mathbb{R}