Question

Given the expression cos(2arccos(2u)), rewrite it in terms of the variable u as an algebraic expression.

A. 4u²−1
B. 2u²−1
C. 2u²+1
D.1−2u²

Answer 1

The given expression cos(2arccos(2u)) can be rewritten as 2u² - 1.

Step-by-step explanation:

This expression can be simplified as follows:

Using the identity: cos(2θ) = 2cos²(θ) - 1

We can rewrite the expression as:

cos(2arccos(2u)) = 2cos²(arccos(2u)) - 1

We know that cos(arccos(x)) = x, so we can substitute arccos(2u) with x:

cos(2arccos(2u)) = 2cos²(x) - 1

Now, we substitute cos²(x) with u:

cos(2arccos(2u)) = 2u² - 1

So, the correct answer is A. 4u²−1.