tan(arcsin x)

sin(arctan x)

Please Help, I have no idea what to do.

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- Sep 9th 2008, 04:27 PMdm10Simplify the trig expression
tan(arcsin x)

sin(arctan x)

Please Help, I have no idea what to do. - Sep 9th 2008, 04:43 PMmr fantastic
Let $\displaystyle \arcsin x = \theta \Rightarrow x = \sin \theta$.

$\displaystyle \tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{x}{\sqrt{1 - x^2}}$.

Therefore $\displaystyle \tan (\arcsin x) = \frac{x}{\sqrt{1 - x^2}}$.

Only the positive root is required (why?).

Try the second one now. - Sep 9th 2008, 04:48 PMProve It