What is cos(arctan(3m)) ?

The solution to cos(arctan(3m)) is (sqrt(1+9m^2))/(1+9m^2)

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simplify cos(arctan(3m))

simplify

cos (arctan (3 m))

\frac{1 + 9 m ^{2}}{1 + 9 m ^{2}}

Solution steps

cos (arctan (3 m))

Use the following identity:

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

= \frac{1 + ( 3 m ) ^{2}}{1 + ( 3 m ) ^{2}}

Simplify

= \frac{1 + 9 m ^{2}}{1 + 9 m ^{2}}

sec (arctan (- \frac{4}{3}) + πn)

tan (θ + 90 0^{\circ})

sec (2) (a x + b) d x

cos (\frac{π}{4} + P)

3 sin (2 x - \frac{π}{6})

What is cos(arctan(3m)) ?
The solution to cos(arctan(3m)) is (sqrt(1+9m^2))/(1+9m^2)