What is cos(arctan(x+0.5)) ?

The solution to cos(arctan(x+0.5)) is (sqrt(x^2+x+1.25))/(x^2+x+1.25)

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simplify cos(arctan(x+0.5))

simplify

cos (arctan (x + 0.5))

\frac{x ^{2} + x + 1.25}{x ^{2} + x + 1.25}

Solution steps

cos (arctan (x + 0.5))

Use the following identity:

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

= \frac{1 + ( x + 0.5 ) ^{2}}{1 + ( x + 0.5 ) ^{2}}

Simplify

= \frac{x ^{2} + x + 1.25}{x ^{2} + x + 1.25}

csc^{2} (- csc^{2} (x))

sin (- 7 π + x)

e^{3 t} cos (t + π)

sin (18 0^{\circ} - (θ + β))

sec (arcsec (e^{x}))

What is cos(arctan(x+0.5)) ?
The solution to cos(arctan(x+0.5)) is (sqrt(x^2+x+1.25))/(x^2+x+1.25)