What is the general solution for sec(-135)-cot(x)=2 ?

The general solution for sec(-135)-cot(x)=2 is x=2.85666…+180n

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sec(-135)-cot(x)=2

Solution

sec (- 13 5^{\circ}) - cot (x) = 2

Solution

x = 2.85666 \dots + 18 0^{\circ} n

Radians

x = 2.85666 \dots + πn

Solution steps

sec (- 13 5^{\circ}) - cot (x) = 2

sec (- 13 5^{\circ}) = - 2

sec (- 13 5^{\circ})

Use the following property:

sec (- x) = sec (x)

sec (- 13 5^{\circ}) = sec (13 5^{\circ})

= sec (13 5^{\circ})

Use the following trivial identity:

sec (13 5^{\circ}) = - 2

sec (13 5^{\circ})

sec (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= - 2

= - 2

- 2 - cot (x) = 2

Move

2

to the right side

- 2 - cot (x) = 2

Add

2

to both sides

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

Simplify

- cot (x) = 2 + 2

- cot (x) = 2 + 2

Divide both sides by

- 1

- cot (x) = 2 + 2

Divide both sides by

- 1

\frac{- cot ( x )}{- 1} = \frac{2}{- 1} + \frac{2}{- 1}

Simplify

\frac{- cot ( x )}{- 1} = \frac{2}{- 1} + \frac{2}{- 1}

Simplify

\frac{- cot ( x )}{- 1} : cot (x)

\frac{- cot ( x )}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{cot ( x )}{1}

Apply rule

\frac{a}{1} = a

= cot (x)

Simplify

\frac{2}{- 1} + \frac{2}{- 1} : - 2 - 2

\frac{2}{- 1} + \frac{2}{- 1}

Apply rule

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

= \frac{2 + 2}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 + 2}{1}

Apply rule

\frac{a}{1} = a

= - (2 + 2)

Distribute parentheses

= - (2) - (2)

Apply minus-plus rules

+ (- a) = - a

= - 2 - 2

cot (x) = - 2 - 2

cot (x) = - 2 - 2

cot (x) = - 2 - 2

Apply trig inverse properties

cot (x) = - 2 - 2

General solutions for

cot (x) = - 2 - 2

cot (x) = - a \Rightarrow x = arccot (- a) + 18 0^{\circ} n

x = arccot (- 2 - 2) + 18 0^{\circ} n

x = arccot (- 2 - 2) + 18 0^{\circ} n

Show solutions in decimal form

x = 2.85666 \dots + 18 0^{\circ} n

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Frequently Asked Questions (FAQ)

What is the general solution for sec(-135)-cot(x)=2 ?
The general solution for sec(-135)-cot(x)=2 is x=2.85666…+180n