What is cos(arctan(-u/g)) ?

The solution to cos(arctan(-u/g)) is (gsqrt(g^2+u^2))/(g^2+u^2)

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simplify cos(arctan(-u/g))

simplify

cos (arctan (- \frac{u}{g}))

\frac{g g ^{2} + u ^{2}}{g ^{2} + u ^{2}}

Solution steps

cos (arctan (- \frac{u}{g}))

Use the following identity:

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

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

Simplify

= \frac{g g ^{2} + u ^{2}}{g ^{2} + u ^{2}}

cos (arcsec (9 x))

cos (θ) + cos (- θ)

sin (- 6 x)

sin (- x) + cos (\frac{π}{2} - x)

tan (arcsin (x - 1))

What is cos(arctan(-u/g)) ?
The solution to cos(arctan(-u/g)) is (gsqrt(g^2+u^2))/(g^2+u^2)