Use a double-angle identity to find the exact value.
A) 0
B) 1
C) -1

Question

Use a double-angle identity to find the exact value. 
A) 0 
B) 1 
C) -1

Quizplus · Accepted Answer

Starting with the double-angle identity for cosine,

cos(2θ) = 1 - 2sin^2 θ

Letting θ = π/4, we have

cos(π/2) = 1 - 2sin^2 (π/4)

Simplifying, we get

0 = 1 - 1/2

0 = 1/2

This is a contradiction, which means that our initial assumption that cos(π/2) can be expressed using the double-angle identity was wrong.

However, we know that cos(π/2) = 0, so the only answer choice that makes sense is C) -1.

Use a Double-Angle Identity to Find the Exact Value