What is cos(arctan(t/R)) ?

The solution to cos(arctan(t/R)) is (Rsqrt(R^2+t^2))/(R^2+t^2)

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simplify cos(arctan(t/R))

simplify

cos (arctan (\frac{t}{R}))

\frac{R R ^{2} + t ^{2}}{R ^{2} + t ^{2}}

Solution steps

cos (arctan (\frac{t}{R}))

Use the following identity:

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

= \frac{1 + ( \frac{t}{R} ) ^{2}}{1 + ( \frac{t}{R} ) ^{2}}

Simplify

= \frac{R R ^{2} + t ^{2}}{R ^{2} + t ^{2}}

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What is cos(arctan(t/R)) ?
The solution to cos(arctan(t/R)) is (Rsqrt(R^2+t^2))/(R^2+t^2)