What is the correct expansion of cos (2x + 3y)
cos(A+B) = cosAcosB - sinAsinB
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To find the correct expansion of cos(2x + 3y), we can use the trigonometric identity known as the cosine double-angle formula. The formula states that cos(2θ) = cos²(θ) - sin²(θ).
In this case, we have 2x + 3y as our angle. To apply the double-angle formula, we need to express it as a multiple of a single angle. We can do this by noting that 2x + 3y is the sum of two angles, 2x and 3y. Therefore, we can rewrite the expression as:
cos(2x + 3y) = cos((2x) + (3y))
Now, we can apply the double-angle formula to each individual angle:
cos(2x) = cos²(x) - sin²(x)
cos(3y) = cos²(y) - sin²(y)
Substituting these values back into the original expression, we have:
cos(2x + 3y) = cos²(x) - sin²(x) + cos²(y) - sin²(y)
And that is the correct expansion of cos(2x + 3y).