Question

write the trigonometric expression as an algebraic expression.

sin (2 arcsin x)

Answer 1

Step 1:

The trigonometric function is

Use double - angle formula : .

           equation (1)

Solve for .

Use inverse trigonometric functions : .

Then .

Step 2:

Solve for .

Consider .

Substitute in the above expression.

From Pythagorean theorem,

.

Substitute in .

.

Step 3:

Substitute and in equation (1).

Solution: