What is tan(arcsin(4/x)) ?

The solution to tan(arcsin(4/x)) is (4sqrt(x^2-16))/(x^2-16)

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simplify tan(arcsin(4/x))

simplify

tan (arcsin (\frac{4}{x}))

\frac{4 x ^{2} - 16}{x ^{2} - 16}

Solution steps

tan (arcsin (\frac{4}{x}))

Use the following identity:

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

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

Simplify

= \frac{4 x ^{2} - 16}{x ^{2} - 16}

\frac{1}{1 + tan ^{2} ( θ )}

sin (x + \frac{2 π}{3})

sin (27 0^{\circ} + θ)

sin (x - \frac{2 π}{3})

- cos (x + π)

What is tan(arcsin(4/x)) ?
The solution to tan(arcsin(4/x)) is (4sqrt(x^2-16))/(x^2-16)