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

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

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

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

\frac{1}{tan ( 1 )}

Refine to a decimal form

= 0.64209 \dots

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}

The two sides are not equal

\Rightarrow False

1 + cos^{2} (x) = 2 cos^{2} (x) + sin^{2} (x)

sec (- x) = \frac{1}{cos ( x )}

csc (x) = 2

sin (x) csc^{2} (x) = \frac{1}{sin ( x )}

\frac{cos ( 2 θ )}{cos ^{2} ( θ )} = 1 - tan^{2} (θ)