What is the general solution for 5cos(x)cot(x)-3cos(x)-10cot(x)+6=0 ?

The general solution for 5cos(x)cot(x)-3cos(x)-10cot(x)+6=0 is x=1.03037…+pin

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Popular Trigonometry >

5cos(x)cot(x)-3cos(x)-10cot(x)+6=0

Solution

5 cos (x) cot (x) - 3 cos (x) - 10 cot (x) + 6 = 0

Solution

x = 1.03037 \dots + πn

Degrees

x = 59.03624 \dots^{\circ} + 18 0^{\circ} n

Solution steps

5 cos (x) cot (x) - 3 cos (x) - 10 cot (x) + 6 = 0

Factor

5 cos (x) cot (x) - 3 cos (x) - 10 cot (x) + 6 : (5 cot (x) - 3) (cos (x) - 2)

5 cos (x) cot (x) - 3 cos (x) - 10 cot (x) + 6

= (5 cot (x) cos (x) - 3 cos (x)) + (- 10 cot (x) + 6)

Factor out

- 2

from

- 10 cot (x) + 6 : - 2 (5 cot (x) - 3)

- 10 cot (x) + 6

Rewrite

6

3 \cdot 2

Rewrite

- 10

5 \cdot 2

= 5 \cdot 2 cot (x) + 3 \cdot 2

Factor out common term

- 2

= - 2 (5 cot (x) - 3)

Factor out

cos (x)

from

5 cot (x) cos (x) - 3 cos (x) : cos (x) (5 cot (x) - 3)

5 cot (x) cos (x) - 3 cos (x)

Factor out common term

cos (x)

= cos (x) (5 cot (x) - 3)

= - 2 (5 cot (x) - 3) + cos (x) (5 cot (x) - 3)

Factor out common term

5 cot (x) - 3

= (5 cot (x) - 3) (cos (x) - 2)

(5 cot (x) - 3) (cos (x) - 2) = 0

Solving each part separately

5 cot (x) - 3 = 0 or cos (x) - 2 = 0

5 cot (x) - 3 = 0 : x = arccot (\frac{3}{5}) + πn

5 cot (x) - 3 = 0

Move

3

to the right side

5 cot (x) - 3 = 0

Add

3

to both sides

5 cot (x) - 3 + 3 = 0 + 3

Simplify

5 cot (x) = 3

5 cot (x) = 3

Divide both sides by

5

5 cot (x) = 3

Divide both sides by

5

\frac{5 cot ( x )}{5} = \frac{3}{5}

Simplify

cot (x) = \frac{3}{5}

cot (x) = \frac{3}{5}

Apply trig inverse properties

cot (x) = \frac{3}{5}

General solutions for

cot (x) = \frac{3}{5}

cot (x) = a \Rightarrow x = arccot (a) + πn

x = arccot (\frac{3}{5}) + πn

x = arccot (\frac{3}{5}) + πn

cos (x) - 2 = 0 :

No Solution

cos (x) - 2 = 0

Move

2

to the right side

cos (x) - 2 = 0

Add

2

to both sides

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

Simplify

cos (x) = 2

cos (x) = 2

- 1 \leq cos (x) \leq 1

No Solution

Combine all the solutions

x = arccot (\frac{3}{5}) + πn

Show solutions in decimal form

x = 1.03037 \dots + πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 5cos(x)cot(x)-3cos(x)-10cot(x)+6=0 ?
The general solution for 5cos(x)cot(x)-3cos(x)-10cot(x)+6=0 is x=1.03037…+pin