What is the value of cos(arctan(1/2)) ?

The value of cos(arctan(1/2)) is (2sqrt(5))/5

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cos(arctan(1/2))

cos (arctan (\frac{1}{2}))

\frac{2 5}{5}

Decimal Notation

0.89442 \dots

Solution steps

cos (arctan (\frac{1}{2}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{2 5}{5}

cos (7 1^{\circ})

4 sin (12 0^{\circ})

cos (arcsin (\frac{1}{3}) - arctan (\frac{1}{2}))

1 - sin (\frac{3 π}{2})

ln (cos (\frac{π}{3}))

What is the value of cos(arctan(1/2)) ?
The value of cos(arctan(1/2)) is (2sqrt(5))/5