Is arccot(x)=tan(x) ?

The answer to whether arccot(x)=tan(x) is False

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prove arccot(x)=tan(x)

prove

arccot (x) = tan (x)

False

Solution steps

arccot (x) = tan (x)

Show that the two sides are not equal

For

arccot (x) = tan (x)

plug in

x = 0

arccot (0) = \frac{π}{2} (Decimal : Degrees : 1.57079 \dots 9 0^{\circ})

arccot (0)

Use the following trivial identity:

arccot (0) = \frac{π}{2}

arccot (0)

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}{2}

= \frac{π}{2}

tan (0) = 0

tan (0)

Use the following trivial identity:

tan (0) = 0

tan (0)

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}

= 0

= 0

The two sides are not equal

\Rightarrow False

cot (θ) + tan (θ) = sec (θ) + csc (θ)

sin (75 0^{\circ}) = sin (45 0^{\circ} + 30 0^{\circ})

2 sin (θ) + sin (2 θ) = 0

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

\frac{2 sin ( x ) cos ( x )}{cos ( x )} = 2