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 Notation

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}

sin (\frac{2 π}{3}) - cos (\frac{π}{12}) + tan (\frac{5 π}{4})

sin (5 0^{\circ}) sin (1 0^{\circ}) - 2 cos (4 0^{\circ}) - 2 cos (2 0^{\circ})

3 sin (\frac{π}{3}) - \frac{1}{2} cos^{2} (\frac{π}{3}) - \frac{7}{8}

cos (\frac{3 π}{4}) + i \cdot sin (\frac{3 π}{4})

cos^{3} (9 0^{\circ})

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