What is tan(arcsin(1/x)) ?

The solution to tan(arcsin(1/x)) is (sqrt(x^2-1))/(x^2-1)

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simplify tan(arcsin(1/x))

simplify

tan (arcsin (\frac{1}{x}))

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

Solution steps

tan (arcsin (\frac{1}{x}))

Use the following identity:

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

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

Simplify

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

sin (2 arctan (\frac{x}{4}))

sin (2 tan^{(- 1)} (x))

tan (arcsec (\frac{2 u}{a}))

3 cos (2 x + \frac{π}{2}) - 3

csc (a - 27 0^{\circ})

What is tan(arcsin(1/x)) ?
The solution to tan(arcsin(1/x)) is (sqrt(x^2-1))/(x^2-1)