Question

Simplify the expression.

sin (tan^-1 x)

Answer 1

Step 1:

The trigonometric expression is .

Consider , then

Definition of inverse trigonometric function : .

If , then .

.

Step 2:

From Pythagorean theorem,

The square of the hypotenuse is equal to sum the squares of the other two sides.

.

Substitute in .

.

Solution :

.