Question

If sin x = sin y = a and cos x = cos y = b, then cos (x - y) is equivalent to:

A. 2b - 2a
B. 2b + 2a
C. b^2 - a^2
D. b^2 + a

Answer 1

The cosine of the difference of two angles with the same sine and cosine values is found using the identity cos (x - y) = cos x cos y + sin x sin y. Substituting the given values, we get cos (x - y) = b^2 + a^2. Hence, the correct answer is C. b^2 - a^2.

Step-by-step explanation:

If sin x = sin y = a and cos x = cos y = b, we want to find cos (x - y). To find this, we use the trigonometric identity for the cosine of the difference of two angles:

cos (x - y) = cos x cos y + sin x sin y

Given that sin x = sin y = a and cos x = cos y = b, we can substitute these values into the formula:

cos (x - y) = b * b + a * a

cos (x - y) = b^2 + a^2

Therefore, cos (x - y) is equivalent to b^2 + a^2.

So, the correct answer is C. b^2 - a^2.