Answered

Get personalized answers to your specific questions with IDNLearn.com. Ask your questions and get detailed, reliable answers from our community of experienced experts.

Write the expression as the sine or cosine of an angle.

[tex]\[
\cos 7y \cos 3y - \sin 7y \sin 3y
\][/tex]

[tex]\[
\cos (7y + 3y)
\][/tex]

Hint: [tex]\(\sin (A \pm B) = \sin A \cos B \pm \cos A \sin B\)[/tex]

[tex]\(\cos (A \pm B) = \cos A \cos B \mp \sin A \sin B\)[/tex]

Sagot :

GinnyAnsweridn
To rewrite the given expression [tex]\(\cos(7y) \cos(3y) - \sin(7y) \sin(3y)\)[/tex] as a single trigonometric function, we can use the trigonometric identities provided. Specifically, we will use the cosine addition identity.

The cosine addition identity states:
[tex]\[ \cos(A \pm B) = \cos(A) \cos(B) \mp \sin(A) \sin(B) \][/tex]

In this identity:
- The plus sign in the argument of the cosine function ([tex]\(\pm\)[/tex]) corresponds to the minus sign between the terms in the expression ([tex]\(\mp\)[/tex]).

Given the expression:
[tex]\[ \cos(7y) \cos(3y) - \sin(7y) \sin(3y) \][/tex]

We need to match this with one of the identities. Specifically, we notice that it fits the form of:
[tex]\[ \cos(A + B) = \cos(A) \cos(B) - \sin(A) \sin(B) \][/tex]

Here, we can see that:
- [tex]\(A = 7y\)[/tex]
- [tex]\(B = 3y\)[/tex]

Therefore, the given expression can be rewritten as:
[tex]\[ \cos(7y + 3y) \][/tex]

Simplifying inside the cosine function:
[tex]\[ \cos(10y) \][/tex]

So, the expression [tex]\(\cos(7y) \cos(3y) - \sin(7y) \sin(3y)\)[/tex] is equivalent to:
[tex]\[ \cos(10y) \][/tex]

Thus, the answer is:
[tex]\[ \cos(10y) \][/tex]
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.