What is the value of cos(arctan(1/4)) ?

The value of cos(arctan(1/4)) is (4sqrt(17))/(17)

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cos(arctan(1/4))

cos (arctan (\frac{1}{4}))

\frac{4 17}{17}

Decimal Notation

0.97014 \dots

Solution steps

cos (arctan (\frac{1}{4}))

Rewrite using trig identities:

cos (arctan (\frac{1}{4})) = \frac{1 + ( \frac{1}{4} ) ^{2}}{1 + ( \frac{1}{4} ) ^{2}}

Use the following identity:

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

= \frac{1 + ( \frac{1}{4} ) ^{2}}{1 + ( \frac{1}{4} ) ^{2}}

= \frac{1 + ( \frac{1}{4} ) ^{2}}{1 + ( \frac{1}{4} ) ^{2}}

Simplify

= \frac{4 17}{17}

cos (- \frac{1 π}{3})

2 + sin (\frac{π}{8})

\frac{60}{sin ( 4 5 ^{\circ} )}

cos (4 5^{\circ}) \cdot 3

cos (144 0^{\circ})

What is the value of cos(arctan(1/4)) ?
The value of cos(arctan(1/4)) is (4sqrt(17))/(17)