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

The value of cos(arctan(1/5)) is (5sqrt(26))/(26)

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cos(arctan(1/5))

cos (arctan (\frac{1}{5}))

\frac{5 26}{26}

Decimal Notation

0.98058 \dots

Solution steps

cos (arctan (\frac{1}{5}))

Rewrite using trig identities:

cos (arctan (\frac{1}{5})) = \frac{1 + ( \frac{1}{5} ) ^{2}}{1 + ( \frac{1}{5} ) ^{2}}

Use the following identity:

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

= \frac{1 + ( \frac{1}{5} ) ^{2}}{1 + ( \frac{1}{5} ) ^{2}}

= \frac{1 + ( \frac{1}{5} ) ^{2}}{1 + ( \frac{1}{5} ) ^{2}}

Simplify

= \frac{5 26}{26}

67 sin (3 5^{\circ})

sin (\frac{π}{45})

arcsin (78792)

- 5 e^{- 5} - \frac{1 ^{3}}{3} + cos (3) \cdot 3 + e^{5} \cdot 1^{4}

arctan (\frac{107.61 - 100}{170.477 - 100})

What is the value of cos(arctan(1/5)) ?
The value of cos(arctan(1/5)) is (5sqrt(26))/(26)