# How do you write sin(arctan(a)) as an expression of "a" not involving any trigonometric functions or their inverses?

##### 1 Answer

Let

Then

So

Hence

#### Explanation:

Having let

Multiply both ends by

Square both sides to get:

Note that this will introduce a spurious solution to be eliminated later.

Add

Divide both sides by

So

Now remember that

Therefore

So the correct solution is