What is the general solution for 24arctan(x)=4pi ?

The general solution for 24arctan(x)=4pi is x=(sqrt(3))/3

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24arctan(x)=4pi

24 arctan (x) = 4 π

x = \frac{3}{3}

Solution steps

24 arctan (x) = 4 π

Divide both sides by

24

24 arctan (x) = 4 π

Divide both sides by

24

\frac{24 arctan ( x )}{24} = \frac{4 π}{24}

Simplify

arctan (x) = \frac{π}{6}

arctan (x) = \frac{π}{6}

Apply trig inverse properties

arctan (x) = \frac{π}{6}

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

x = tan (\frac{π}{6})

tan (\frac{π}{6}) = \frac{3}{3}

tan (\frac{π}{6})

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

tan (\frac{π}{6})

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}

= \frac{3}{3}

= \frac{3}{3}

x = \frac{3}{3}

x = \frac{3}{3}

cos^{2} (x) - sin (x) - 1 = 0

5 cos (x) + 12 sin (x) = 6

- 73 tan (θ) + 5 = 26

6 sin (x) = cos (x) - 3

- 2 sin (4 x) = 0

What is the general solution for 24arctan(x)=4pi ?
The general solution for 24arctan(x)=4pi is x=(sqrt(3))/3