How do you solve tan(sin^-1 x/2)? (show steps)

First: Equations are solved. is an expression, and expressions can be simplified.

Now suppose . Imagine a right triangle with one angle (not the one opposite the hypotenuse, of course) labeled . This relation suggests that

and under the hood, we're assuming that , because otherwise we wouldn't be able to properly alternate from to so seamlessly.

Now,

so the given expression is the same as the tangent of that same angle .

If , then in the triangle, the leg opposite the angle occurs with the length of the hypotenuse in a ratio of to 2. By the Pythagorean theorem, the remaining side - call it - satisifies

and we have

tangent

step-by-step explanation: