What is tan(arcsin(5x)) ?

The solution to tan(arcsin(5x)) is (5xsqrt(1-25x^2))/(1-25x^2)

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simplify tan(arcsin(5x))

simplify

tan (arcsin (5 x))

\frac{5 x 1 - 25 x ^{2}}{1 - 25 x ^{2}}

Solution steps

tan (arcsin (5 x))

Use the following identity:

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

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

Simplify

= \frac{5 x 1 - 25 x ^{2}}{1 - 25 x ^{2}}

csc (arctan (2 x + 1))

sin (arccos (u))

2 sin (2 x - \frac{π}{4}) + 1

- sin (\cdot (- sin (x)))

cos^{2} (x + \frac{π}{2})

What is tan(arcsin(5x)) ?
The solution to tan(arcsin(5x)) is (5xsqrt(1-25x^2))/(1-25x^2)