What is the value of cos(arctan(5/12)) ?

The value of cos(arctan(5/12)) is 12/13

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cos(arctan(5/12))

cos (arctan (\frac{5}{12}))

\frac{12}{13}

Decimal Notation

0.92307 \dots

Solution steps

cos (arctan (\frac{5}{12}))

Rewrite using trig identities:

cos (arctan (\frac{5}{12})) = \frac{1 + ( \frac{5}{12} ) ^{2}}{1 + ( \frac{5}{12} ) ^{2}}

Use the following identity:

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

= \frac{1 + ( \frac{5}{12} ) ^{2}}{1 + ( \frac{5}{12} ) ^{2}}

= \frac{1 + ( \frac{5}{12} ) ^{2}}{1 + ( \frac{5}{12} ) ^{2}}

Simplify

= \frac{12}{13}

cos (7 5^{\circ}) cos (1 5^{\circ})

tan (4 5^{\circ} - 3 0^{\circ})

sec (1 1^{\circ})

csc (- 45 0^{\circ})

arccos (0.72)

What is the value of cos(arctan(5/12)) ?
The value of cos(arctan(5/12)) is 12/13