# Write the following functions in simplest form.

$$\arctan\left(\frac{x}{\sqrt{a^2-x^2}}\right)$$

Hi, I am not able to solve this problem from last 1 hour. Please help me to solve this question. As I can solve simple inverse trigonometric functions.

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Set $x = a \sin(\phi)$, and simplify the argument of the $\arctan$. Are you assuming $0<x<a$? – Sasha Aug 23 '12 at 15:38

Think geometrically. What is the $\tan(\phi)$ ?
So $\arctan\dfrac{x}{\sqrt{a^2-x^2}}=\arccos\dfrac x a$. – Michael Hardy Aug 23 '12 at 20:46
@MichaelHardy I think it should be $\arcsin \frac{x}{a}$, instead. – Sasha Aug 23 '12 at 21:01