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

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

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simplify tan(arcsin(x/2))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

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

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sin (arctan (\frac{y}{x}))

cos (18 0^{\circ} - θ)

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