What is tan(arcsin(x/5)) ?

The solution to tan(arcsin(x/5)) is (xsqrt(25-x^2))/(25-x^2)

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simplify tan(arcsin(x/5))

simplify

tan (arcsin (\frac{x}{5}))

\frac{x 25 - x ^{2}}{25 - x ^{2}}

Solution steps

tan (arcsin (\frac{x}{5}))

Use the following identity:

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

= \frac{( \frac{x}{5} ) 1 - ( \frac{x}{5} ) ^{2}}{1 - ( \frac{x}{5} ) ^{2}}

Simplify

= \frac{x 25 - x ^{2}}{25 - x ^{2}}

cos (π - nπ)

4 - 4 sin^{2} (x)

cos (arcsin (\frac{x}{5}))

sin (θ + 2 π)

- cos (- x)

What is tan(arcsin(x/5)) ?
The solution to tan(arcsin(x/5)) is (xsqrt(25-x^2))/(25-x^2)