What is the general solution for 3arctan(x)=pi ?

The general solution for 3arctan(x)=pi is x=sqrt(3)

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3arctan(x)=pi

3 arctan (x) = π

x = 3

Solution steps

3 arctan (x) = π

Divide both sides by

3

3 arctan (x) = π

Divide both sides by

3

\frac{3 arctan ( x )}{3} = \frac{π}{3}

Simplify

arctan (x) = \frac{π}{3}

arctan (x) = \frac{π}{3}

Apply trig inverse properties

arctan (x) = \frac{π}{3}

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

x = tan (\frac{π}{3})

tan (\frac{π}{3}) = 3

tan (\frac{π}{3})

Use the following trivial identity:

tan (\frac{π}{3}) = 3

tan (\frac{π}{3})

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 3

= 3

x = 3

x = 3

cot (x) (tan (x) + 3) = 0

1 - cos (x) = 2 sin^{2} (x)

- cos (x - π) = \frac{3}{2}

cos^{4} (x) = 8 cos^{4} (x) - 8 cos^{2} (x) + 1

sin^{2} (x + \frac{π}{2}) = \frac{3}{4}

What is the general solution for 3arctan(x)=pi ?
The general solution for 3arctan(x)=pi is x=sqrt(3)