What is the general solution for 30arctan(x)=5pi ?

The general solution for 30arctan(x)=5pi is x=(sqrt(3))/3

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30arctan(x)=5pi

30 arctan (x) = 5 π

x = \frac{3}{3}

Solution steps

30 arctan (x) = 5 π

Divide both sides by

30

30 arctan (x) = 5 π

Divide both sides by

30

\frac{30 arctan ( x )}{30} = \frac{5 π}{30}

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}

cosh (2 x) - 10 cosh (x) + 13 = 0

3 sin (x) - sin (2 x) = 0

7 cos^{2} (x) + 14 cos (x) + 7 = 0

θ, 2 sin (θ) = 2 cos (2 θ)

sec (θ) + 4 = 4 sec (θ)

What is the general solution for 30arctan(x)=5pi ?
The general solution for 30arctan(x)=5pi is x=(sqrt(3))/3