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

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

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

\frac{1}{arctan ( 1 )} = \frac{4}{π} (Decimal : Degrees : 1.27323 \dots 72.9 5^{\circ})

\frac{1}{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{1}{\frac{π}{4}}

Simplify

= \frac{4}{π}

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

arccot (1)

Use the following trivial identity:

arccot (1) = \frac{π}{4}

arccot (1)

x - 3 - 1 - \frac{3}{3} 0 \frac{3}{3} 13 arccot (x) \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} arccot (x) 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ}

= \frac{π}{4}

= \frac{π}{4}

The two sides are not equal

\Rightarrow False

\frac{1}{sin ( θ ) cos ( θ )} - tan (θ) = cot (θ)

(- sin (x)) (3 cos (x)) = - 3 sin (x) cos (x)

cot (θ) \cdot sec (θ) = \frac{1}{cos ( θ )}

sin (x) sin (y) = 2 sin (\frac{x + y}{2}) cos (\frac{x - y}{2})

1 - sin (x) \cdot cos (x) \cdot tan (x) = cos^{2} (x)

Is 1/(arctan(x))=arccot(x) ?
The answer to whether 1/(arctan(x))=arccot(x) is False