What is cos(arctan(sqrt(7x^3))) ?

The solution to cos(arctan(sqrt(7x^3))) is (sqrt(1+7x^3))/(1+7x^3)

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simplify cos(arctan(sqrt(7x^3)))

simplify

cos (arctan (7 x^{3}))

\frac{1 + 7 x ^{3}}{1 + 7 x ^{3}}

Solution steps

cos (arctan (7 x^{3}))

Use the following identity:

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

= \frac{1 + ( 7 x ^{3} ) ^{2}}{1 + ( 7 x ^{3} ) ^{2}}

Simplify

= \frac{1 + 7 x ^{3}}{1 + 7 x ^{3}}

sec (\frac{25 π}{2} - x)

cos (cos^{2} (x) - 1)

sin (arcsin (\frac{y}{x}))

- sin (nπ)

1 - sin (θ) cos (9 0^{\circ} - θ)

What is cos(arctan(sqrt(7x^3))) ?
The solution to cos(arctan(sqrt(7x^3))) is (sqrt(1+7x^3))/(1+7x^3)