What is cos(arctan(D/C)) ?

The solution to cos(arctan(D/C)) is (Csqrt(C^2+D^2))/(C^2+D^2)

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simplify cos(arctan(D/C))

simplify

cos (arctan (\frac{D}{C}))

\frac{C C ^{2} + D ^{2}}{C ^{2} + D ^{2}}

Solution steps

cos (arctan (\frac{D}{C}))

Use the following identity:

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

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

Simplify

= \frac{C C ^{2} + D ^{2}}{C ^{2} + D ^{2}}

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What is cos(arctan(D/C)) ?
The solution to cos(arctan(D/C)) is (Csqrt(C^2+D^2))/(C^2+D^2)