What is csc(arctan(6x)) ?

The solution to csc(arctan(6x)) is (sqrt(1+36x^2))/(6x)

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simplify csc(arctan(6x))

simplify

csc (arctan (6 x))

\frac{1 + 36 x ^{2}}{6 x}

Solution steps

csc (arctan (6 x))

Use the following identity:

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

= \frac{1 + ( 6 x ) ^{2}}{6 x}

1 + (6 x)^{2} = 1 + 36 x^{2}

= \frac{1 + 36 x ^{2}}{6 x}

csc (arcsin (\frac{1}{3}) + 2 πn)

5 sin (2 x - \frac{π}{4}) + cos (2 x)

sin (18 0^{0} - β)

- cos (4 (\frac{π}{2}) + x)

sin^{2} (2 π x) + cos^{2} (2 π x)

What is csc(arctan(6x)) ?
The solution to csc(arctan(6x)) is (sqrt(1+36x^2))/(6x)