Let x and y be angles such that sin(x + y) = 0 and cos(x - y) = 1. What is the value of the expression: (cos x + cos y)² + (sin x - sin y)²?
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Correct answer: A
Explanation
(cosx + cosy)² + (sinx − siny)² = 2 + 2cos(x + y)
sin(x + y) = 0 and cos(x − y) = 1
According to the principal value x + y = 0
cos(x + y) = 1
= 2 + 2 × 1
= 4