Which expression is identical to cos(2*x) / (cos(x) + sin(x)) where defined?
Answer and explanation
Correct answer: A. cos(x) - sin(x)
- Step 1: Expand cos(2*x) as cos(x)^2 - sin(x)^2.
- Step 2: Factor as (cos(x) - sin(x))(cos(x) + sin(x)).
- Step 3: Cancel the common denominator term to obtain cos(x) - sin(x).
Answer
cos(x) - sin(x).
Why not the others: cos(x) + sin(x) results if dividing by cos(x) - sin(x); tan(x) - 1 omits the cosine numerator term; 1 - 2sin(x) confuses the identity with cos(2x) expanded in terms of sin.
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