What is cos(arctan(a/b)) ?

The solution to cos(arctan(a/b)) is (bsqrt(b^2+a^2))/(b^2+a^2)

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simplify cos(arctan(a/b))

simplify

cos (arctan (\frac{a}{b}))

\frac{b b ^{2} + a ^{2}}{b ^{2} + a ^{2}}

Solution steps

cos (arctan (\frac{a}{b}))

Use the following identity:

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

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

Simplify

= \frac{b b ^{2} + a ^{2}}{b ^{2} + a ^{2}}

2 sin (x - \frac{π}{3})

tan (arccos (\frac{y}{7}))

sec (x + π)

tan (27 0^{\circ} + a)

tan (sin (- 1 x))

What is cos(arctan(a/b)) ?
The solution to cos(arctan(a/b)) is (bsqrt(b^2+a^2))/(b^2+a^2)