What is tan(arcsin(2/(3x))) ?

The solution to tan(arcsin(2/(3x))) is (2sqrt(9x^2-4))/(9x^2-4)

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simplify tan(arcsin(2/(3x)))

simplify

tan (arcsin (\frac{2}{3 x}))

\frac{2 9 x ^{2} - 4}{9 x ^{2} - 4}

Solution steps

tan (arcsin (\frac{2}{3 x}))

Use the following identity:

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

= \frac{( \frac{2}{3 x} ) 1 - ( \frac{2}{3 x} ) ^{2}}{1 - ( \frac{2}{3 x} ) ^{2}}

Simplify

= \frac{2 9 x ^{2} - 4}{9 x ^{2} - 4}

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What is tan(arcsin(2/(3x))) ?
The solution to tan(arcsin(2/(3x))) is (2sqrt(9x^2-4))/(9x^2-4)