What is cos(arctan(x+2)) ?

The solution to cos(arctan(x+2)) is (sqrt(x^2+4x+5))/(x^2+4x+5)

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simplify cos(arctan(x+2))

simplify

cos (arctan (x + 2))

\frac{x ^{2} + 4 x + 5}{x ^{2} + 4 x + 5}

Solution steps

cos (arctan (x + 2))

Use the following identity:

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

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

Simplify

= \frac{x ^{2} + 4 x + 5}{x ^{2} + 4 x + 5}

- tan (- x)

3 sin (5 x - \frac{π}{2})

3 sin (θ - \frac{π}{2})

sin (2 x + 2 x)

sin (108 0^{\circ} + x)

What is cos(arctan(x+2)) ?
The solution to cos(arctan(x+2)) is (sqrt(x^2+4x+5))/(x^2+4x+5)