What is cos(arctan(2/x)) ?

The solution to cos(arctan(2/x)) is (xsqrt(x^2+4))/(x^2+4)

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simplify cos(arctan(2/x))

simplify

cos (arctan (\frac{2}{x}))

\frac{x x ^{2} + 4}{x ^{2} + 4}

Solution steps

cos (arctan (\frac{2}{x}))

Use the following identity:

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

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

Simplify

= \frac{x x ^{2} + 4}{x ^{2} + 4}

3 csc (2) (t) - 6 e t d t

sin (- \frac{π}{2} + φ)

sin (π - t) + 2 sin (- (2 π - t))

sin (- 1 (2 x^{2} x))

2 cos^{2} (x - π)

What is cos(arctan(2/x)) ?
The solution to cos(arctan(2/x)) is (xsqrt(x^2+4))/(x^2+4)