What is the value of cos(arccot(2)) ?

The value of cos(arccot(2)) is (2sqrt(5))/5

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cos(arccot(2))

cos (arccot (2))

\frac{2 5}{5}

Decimal

0.89442 \dots

Solution steps

cos (arccot (2))

Rewrite using trig identities:

cos (arccot (2)) = \frac{2 1 + 2 ^{2}}{1 + 2 ^{2}}

Use the following identity:

cos (arccot (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

= \frac{2 1 + 2 ^{2}}{1 + 2 ^{2}}

= \frac{2 1 + 2 ^{2}}{1 + 2 ^{2}}

Simplify

= \frac{2 5}{5}

What is the value of cos(arccot(2)) ?
The value of cos(arccot(2)) is (2sqrt(5))/5