What is cos(arctan(y/L)) ?

The solution to cos(arctan(y/L)) is (Lsqrt(L^2+y^2))/(L^2+y^2)

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simplify cos(arctan(y/L))

simplify

cos (arctan (\frac{y}{L}))

\frac{L L ^{2} + y ^{2}}{L ^{2} + y ^{2}}

Solution steps

cos (arctan (\frac{y}{L}))

Use the following identity:

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

= \frac{1 + ( \frac{y}{L} ) ^{2}}{1 + ( \frac{y}{L} ) ^{2}}

Simplify

= \frac{L L ^{2} + y ^{2}}{L ^{2} + y ^{2}}

3 cos (π t + \frac{π}{4})

ln (cos (- x))

cos (\frac{- 7 x}{6})

2 \cdot sin (\frac{π}{3} + x) + 6

\frac{sin ( 2 π x )}{sin ( x )}

What is cos(arctan(y/L)) ?
The solution to cos(arctan(y/L)) is (Lsqrt(L^2+y^2))/(L^2+y^2)