Question

Rewrite tan arcsin as an algebraic expression of x

A.√(1-x²)/x
B.x/√1-x²
C.√(1-x²)
D.1/√(1-x²)

Answer 1

The algebraic expression for tan(arcsin(x)) is x / √(1 - x²), which means the correct answer is option B.

Step-by-step explanation:

To rewrite tan(arcsin(x)) as an algebraic expression of x, we need to use some trigonometric identities and the concept of a right triangle.

Let's consider a right triangle where the angle θ has a sine value of x. Since sin(θ) = x, this means that the opposite side of angle θ is x and the hypotenuse is 1. By the Pythagorean theorem, the adjacent side is √(1 - x²).

tan(θ) is the ratio of the opposite side to the adjacent side, so we get:

tan(θ) = οpposite/οβjacent = x / √(1 - x²)

Therefore, tan(arcsin(x)) = x / √(1 - x²), which corresponds to answer choice B.