What is csc(arctan(2x+1)) ?

The solution to csc(arctan(2x+1)) is (sqrt(4x^2+4x+2))/(2x+1)

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simplify csc(arctan(2x+1))

simplify

csc (arctan (2 x + 1))

\frac{4 x ^{2} + 4 x + 2}{2 x + 1}

Solution steps

csc (arctan (2 x + 1))

Use the following identity:

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

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

Simplify

= \frac{4 x ^{2} + 4 x + 2}{2 x + 1}

sin (arccos (u))

2 sin (2 x - \frac{π}{4}) + 1

- sin (\cdot (- sin (x)))

cos^{2} (x + \frac{π}{2})

sin (arcsec (\frac{x}{6}))

What is csc(arctan(2x+1)) ?
The solution to csc(arctan(2x+1)) is (sqrt(4x^2+4x+2))/(2x+1)