What is sec(arccsc(x/4)) ?

The solution to sec(arccsc(x/4)) is (xsqrt(x^2-16))/(x^2-16)

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simplify sec(arccsc(x/4))

simplify

sec (arccsc (\frac{x}{4}))

\frac{x x ^{2} - 16}{x ^{2} - 16}

Solution steps

sec (arccsc (\frac{x}{4}))

Use the following identity:

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

= \frac{( \frac{x}{4} ) ( \frac{x}{4} ) ^{2} - 1}{( \frac{x}{4} ) ^{2} - 1}

Simplify

= \frac{x x ^{2} - 16}{x ^{2} - 16}

\frac{e ^{x}}{sin ( x )}

sin (t - 2 π)

sec (arcsin (u))

sin (3 π - x)

1 + cot (x - 3 \frac{π}{2})

What is sec(arccsc(x/4)) ?
The solution to sec(arccsc(x/4)) is (xsqrt(x^2-16))/(x^2-16)