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Problem 70 Hard Difficulty

Simplify the expression.

$ \tan (\sin^{-1} x) $

Answer

$\tan (y)=\frac{x}{\sqrt{1-x^{2}}}$

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Video Transcript

okay. We want to simplify this expression. Tangent of inverse sign of X in verse. Sign of X means the angle. Who signed his ex? I'm going to call that angle theta, so let's draw a reference triangle for data. So let's suppose this is angle Fada and we know it's sign is X. That means the opposite over high pot news is X so we could make the opposite X and the high pot noose. One X divided by one is X. Now we need the tangent of angle. Fada tangent is opposite over adjacent, so we need to find the length of the adjacent for right now I'm going to call it a and I'm going to use the Pythagorean theorem to find it. A squared plus X squared equals one squared, so a squared equals one minus X squared. So a is the square root of one minus X squared. All right, so now the tangent of that angle is the opposite X over the adjacent square root of one minus X squared