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Numerade Educator

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Problem 71 Hard Difficulty

Simplify the expression.

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

Answer

$\frac{x}{\sqrt{1+x^{2}}}$

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Video Transcript

Let's find the sign of angers tension X So inverse tangent X means the angle Whose tangent is X and I'm gonna call that angle Fate up now let's draw picture. Suppose we have angle fatal here and we know it's tangent is X that means the opposite over adjacent is X. So if the opposite was X and the adjacent was one, that ratio would be X. Now, if that's the case, what's the length of the high pot news? If we're going to find the sine of the angle, we're going to need the high pot news as well as the opposite. So for now, I'm going to call the high pot news H. And now I'm going to use the Pythagorean theorem to find it. H squared equals one squared plus X squared. So H is the square root of one plus x squared. Okay, so now I confined the sign of angle fada. It would be opposite which is X over high pot news, which is square root of one plus X squared