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

The solution to cos(arctan(-1/g)) is (gsqrt(g^2+1))/(g^2+1)

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simplify cos(arctan(-1/g))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

cos (8 π + θ)

1 - cos^{2} (t)

1 + tan^{2} (\frac{π}{2} - x)

- sin (x - \frac{π}{2})

cos (arcsin (17 x))

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