What is cos(arctan((-1)/(mg))) ?

The solution to cos(arctan((-1)/(mg))) is (mgsqrt(m^2g^2+1))/(m^2g^2+1)

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simplify cos(arctan((-1)/(mg)))

simplify

cos (arctan (\frac{- 1}{m g}))

\frac{m g m ^{2} g ^{2} + 1}{m ^{2} g ^{2} + 1}

Solution steps

cos (arctan (\frac{- 1}{m g}))

Use the following identity:

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

= \frac{1 + ( \frac{- 1}{m g} ) ^{2}}{1 + ( \frac{- 1}{m g} ) ^{2}}

Simplify

= \frac{m g m ^{2} g ^{2} + 1}{m ^{2} g ^{2} + 1}

sin (arcsin (a x))

4 sin (12 0^{\circ} - x)

2 tan (x - \frac{π}{4}) - 2

cos (π + kπ)

\frac{sin ( - 3 x )}{sin ( 9 x )}

What is cos(arctan((-1)/(mg))) ?
The solution to cos(arctan((-1)/(mg))) is (mgsqrt(m^2g^2+1))/(m^2g^2+1)