What is the general solution for 3arctan(2x)=pi ?

The general solution for 3arctan(2x)=pi is x=(sqrt(3))/2

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3arctan(2x)=pi

3 arctan (2 x) = π

x = \frac{3}{2}

Solution steps

3 arctan (2 x) = π

Divide both sides by

3

3 arctan (2 x) = π

Divide both sides by

3

\frac{3 arctan ( 2 x )}{3} = \frac{π}{3}

Simplify

arctan (2 x) = \frac{π}{3}

arctan (2 x) = \frac{π}{3}

Apply trig inverse properties

arctan (2 x) = \frac{π}{3}

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

2 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

2 x = 3

2 x = 3

Solve

2 x = 3 : x = \frac{3}{2}

2 x = 3

Divide both sides by

2

2 x = 3

Divide both sides by

2

\frac{2 x}{2} = \frac{3}{2}

Simplify

x = \frac{3}{2}

x = \frac{3}{2}

x = \frac{3}{2}

sin (x) - 9 = cos (x) - 9

7 sin (x) + 1 = 5 sin (x)

sec (x) + tan (x) = 1, (0, 2 π)

cos^{2} (θ) - cos (θ) - 20 = 0

100.0191 = 180 - arctan (\frac{3.9254}{0.6936 - x})

What is the general solution for 3arctan(2x)=pi ?
The general solution for 3arctan(2x)=pi is x=(sqrt(3))/2