What is sin(arccos(1/x)) ?

The solution to sin(arccos(1/x)) is (sqrt(x^2-1))/x

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simplify sin(arccos(1/x))

simplify

sin (arccos (\frac{1}{x}))

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

Solution steps

sin (arccos (\frac{1}{x}))

Use the following identity:

sin (arccos (x)) = 1 - x^{2}

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

Simplify

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

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