What is the general solution for 8arctan(x)=2pi ?

The general solution for 8arctan(x)=2pi is x=1

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8arctan(x)=2pi

8 arctan (x) = 2 π

x = 1

Solution steps

8 arctan (x) = 2 π

Divide both sides by

8

8 arctan (x) = 2 π

Divide both sides by

8

\frac{8 arctan ( x )}{8} = \frac{2 π}{8}

Simplify

arctan (x) = \frac{π}{4}

arctan (x) = \frac{π}{4}

Apply trig inverse properties

arctan (x) = \frac{π}{4}

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

x = tan (\frac{π}{4})

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

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}

= 1

= 1

x = 1

x = 1

What is the general solution for 8arctan(x)=2pi ?
The general solution for 8arctan(x)=2pi is x=1