Question

Multiply; then use fundamental identities to simplify the expression below and determine which of the following is NOT equivalent(2-2cosx)(2+2cosx)a. 4-4cos^2xb.4-cos^2xc.4/csc^2xe. 4/1+cot^2xDISCLAIMER: the answer is b. However i am unsure on how that answer was gotten.

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

(2-2cosx)(2+2cosx)

expression not equivalent = ?

Step 02:

We must apply the following property:

(a + b)(a - b) = a² - b²

a = 2

b = 2cosx

(2-2cosx)(2+2cosx) = 2² - (2Cosx)²

= 4 - 4Cos²x

(2-2cosx)(2+2cosx) = 4 - 4Cos²x

Step 03:

We check the options.

a. 4-4cos²x ===> True

b. 4-cos²x ====> False

c. 4/csc^2x ====> True

4 - 4Cos²x = 4 (1 - Cos²x)

= 4 / Csc²x

d. 4/1+cot^2x ===> True

4 - 4Cos²x = 4 (1 - Cos²x)

= 4 / Csc²x

= 4 / (1 + Cot²x)

The answer is:

b. 4 - Cos²x

The expression is not equivalent.