What is the value of cos(arctan(sqrt(2))) ?

The value of cos(arctan(sqrt(2))) is (sqrt(3))/3

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cos(arctan(sqrt(2)))

cos (arctan (2))

\frac{3}{3}

Decimal

0.57735 \dots

Solution steps

cos (arctan (2))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{3}{3}

What is the value of cos(arctan(sqrt(2))) ?
The value of cos(arctan(sqrt(2))) is (sqrt(3))/3