Is arctan(x)= 1/(tan(x)) ?

The answer to whether arctan(x)= 1/(tan(x)) is False

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prove arctan(x)= 1/(tan(x))

prove

arctan (x) = \frac{1}{tan ( x )}

False

Solution steps

arctan (x) = \frac{1}{tan ( x )}

Show that the two sides are not equal

For

arctan (x) = \frac{1}{tan ( x )}

plug in

x = 1

arctan (1) = \frac{π}{4} (Decimal : Degrees : 0.78539 \dots 4 5^{\circ})

arctan (1)

Use the following trivial identity:

arctan (1) = \frac{π}{4}

arctan (1)

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= \frac{π}{4}

= \frac{π}{4}

\frac{1}{tan ( 1 )} = 0.64209 \dots

\frac{1}{tan ( 1 )}

Refine to a decimal form

= 0.64209 \dots

The two sides are not equal

\Rightarrow False