What is sec(arccsc(3x)) ?

The solution to sec(arccsc(3x)) is (3xsqrt(9x^2-1))/(9x^2-1)

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simplify sec(arccsc(3x))

simplify

sec (arccsc (3 x))

\frac{3 x 9 x ^{2} - 1}{9 x ^{2} - 1}

Solution steps

sec (arccsc (3 x))

Use the following identity:

sec (arccsc (x)) = \frac{x x ^{2} - 1}{x ^{2} - 1}

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

Simplify

= \frac{3 x 9 x ^{2} - 1}{9 x ^{2} - 1}

2 cos (u + \frac{π}{3})

cos (x - 6 0^{\circ})

2 sin (x - \frac{π}{2})

- sin (arccos (x))

sin (arctan (2 a))

What is sec(arccsc(3x)) ?
The solution to sec(arccsc(3x)) is (3xsqrt(9x^2-1))/(9x^2-1)