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Chapter 5: Problem 36

Write the expression as the sine, cosine, or tangent of an angle. $$\cos 3 x \cos 2 y+\sin 3 x \sin 2 y$$

Short Answer

Expert verified
The expression \( \cos 3x \cos 2y+ \sin 3x \sin 2y \) can be written in terms of the cosine function as \( \cos(3x + 2y) \)

Step by step solution

01

Recognize the trigonometric identity

First recognize the trigonometric identity \( \cos(A+B)= \cos A \cos B+ \sin A \sin B \). If you look closely, the given expression appears to be in this format.
02

Identify A and B

From the given expression, identify variables that can be represented as A and B. In our case, these would be 3x and 2y.
03

Apply the identity

Now, taking A as \(3x\) and B as \(2y\), our given expression \( \cos 3x \cos 2y+\sin 3x \sin 2y \) can be written as \( \cos(A + B) = \cos(3x + 2y) \)

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Most popular questions from this chapter

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