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

The solution to cos(arctan(d/a)) is (asqrt(a^2+d^2))/(a^2+d^2)

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simplify cos(arctan(d/a))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

tan (\frac{π}{4} - \frac{x}{2})

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cos (arctan (x + 0.5))

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What is cos(arctan(d/a)) ?
The solution to cos(arctan(d/a)) is (asqrt(a^2+d^2))/(a^2+d^2)