What is cos(arccsc(sqrt(x^2-1))) ?

The solution to cos(arccsc(sqrt(x^2-1))) is sqrt((x^2-2)/(x^2-1))

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simplify cos(arccsc(sqrt(x^2-1)))

simplify

cos (arccsc (x^{2} - 1))

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

Solution steps

cos (arccsc (x^{2} - 1))

Use the following identity:

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

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

Simplify

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

36 sec^{2} (x) - 36

\frac{2 x}{sin ( x )} + 1 - π

- e^{- π} sin (nπ) - e^{π} sin (nπ)

cos (x) 1 + tan^{2} (x)

4 cos (t - 2 π)

What is cos(arccsc(sqrt(x^2-1))) ?
The solution to cos(arccsc(sqrt(x^2-1))) is sqrt((x^2-2)/(x^2-1))