Question

Which expression is equivalent to 3cos²(θ/2) - 3?

a. 3/2(cos(θ) - 1)
b. 3/2(cos(θ) - 5)
c. 3(cos(θ) + 2)
d. 3(cos(θ) + 1)

Answer 1

The expression that is equivalent to 3cos²(θ/2) - 3 is 3(cos(θ) + 1).

Step-by-step explanation:

The expression that is equivalent to 3cos²(θ/2) - 3 is option d. 3(cos(θ) + 1).

To simplify, we can use the identity cos²(θ) = 1/2(cos(2θ) + 1). So, the expression becomes 3(1/2(cos(θ) + 1/2 + 1) - 3 = 3(1/2cos(θ) + 3/2 - 3 = 3(cos(θ) + 1).