What is the general solution for (arctan(x)+1)/3 = 1/6 ?

The general solution for (arctan(x)+1)/3 = 1/6 is x=-tan(1/2)

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(arctan(x)+1)/3 = 1/6

Solution

\frac{arctan ( x ) + 1}{3} = \frac{1}{6}

Solution

x = - tan (\frac{1}{2})

Solution steps

\frac{arctan ( x ) + 1}{3} = \frac{1}{6}

Multiply both sides by

3

\frac{arctan ( x ) + 1}{3} = \frac{1}{6}

Multiply both sides by

3

\frac{3 ( arctan ( x ) + 1 )}{3} = \frac{1 \cdot 3}{6}

Simplify

\frac{3 ( arctan ( x ) + 1 )}{3} = \frac{1 \cdot 3}{6}

Simplify

\frac{3 ( arctan ( x ) + 1 )}{3} : arctan (x) + 1

\frac{3 ( arctan ( x ) + 1 )}{3}

Divide the numbers:

\frac{3}{3} = 1

= arctan (x) + 1

Simplify

\frac{1 \cdot 3}{6} : \frac{1}{2}

\frac{1 \cdot 3}{6}

Multiply the numbers:

1 \cdot 3 = 3

= \frac{3}{6}

Cancel the common factor:

3

= \frac{1}{2}

arctan (x) + 1 = \frac{1}{2}

arctan (x) + 1 = \frac{1}{2}

arctan (x) + 1 = \frac{1}{2}

Move

1

to the right side

arctan (x) + 1 = \frac{1}{2}

Subtract

1

from both sides

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

Simplify

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

Simplify

arctan (x) + 1 - 1 : arctan (x)

arctan (x) + 1 - 1

Add similar elements:

1 - 1 = 0

= arctan (x)

Simplify

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

\frac{1}{2} - 1

Convert element to fraction:

1 = \frac{1 \cdot 2}{2}

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

Since the denominators are equal, combine the fractions:

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

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

- 1 \cdot 2 + 1 = - 1

- 1 \cdot 2 + 1

Multiply the numbers:

1 \cdot 2 = 2

= - 2 + 1

Add/Subtract the numbers:

- 2 + 1 = - 1

= - 1

= \frac{- 1}{2}

Apply the fraction rule:

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

= - \frac{1}{2}

arctan (x) = - \frac{1}{2}

arctan (x) = - \frac{1}{2}

arctan (x) = - \frac{1}{2}

Apply trig inverse properties

arctan (x) = - \frac{1}{2}

arctan (x) = a \Rightarrow x = tan (a)

x = tan (- \frac{1}{2})

tan (- \frac{1}{2}) = - tan (\frac{1}{2})

tan (- \frac{1}{2})

Use the following property:

tan (- x) = - tan (x)

tan (- \frac{1}{2}) = - tan (\frac{1}{2})

= - tan (\frac{1}{2})

x = - tan (\frac{1}{2})

x = - tan (\frac{1}{2})

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for (arctan(x)+1)/3 = 1/6 ?
The general solution for (arctan(x)+1)/3 = 1/6 is x=-tan(1/2)