cos(A+ B) cos² A – sin? B sec(A – B) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Prove identity. by choosing one side and manipulate until you arrive at other side.
![The given mathematical equation is:
\[ \sec(A - B) = \frac{\cos(A + B)}{\cos^2 A - \sin^2 B} \]
### Explanation:
- **sec(A - B):** This represents the secant of the difference between angles A and B.
- **cos(A + B):** This is the cosine of the sum of angles A and B.
- **cos²A - sin²B:** This expression involves squaring the cosine of angle A and sine of angle B and then subtracting the latter from the former.
This equation is part of trigonometric identities and can be useful in simplifying expressions or solving trigonometric equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffad5d1f8-d31f-495b-9e28-9b5493232733%2Ffb9cd563-2a35-48cc-9469-558d14d1de3e%2Frjwfct_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The given mathematical equation is:
\[ \sec(A - B) = \frac{\cos(A + B)}{\cos^2 A - \sin^2 B} \]
### Explanation:
- **sec(A - B):** This represents the secant of the difference between angles A and B.
- **cos(A + B):** This is the cosine of the sum of angles A and B.
- **cos²A - sin²B:** This expression involves squaring the cosine of angle A and sine of angle B and then subtracting the latter from the former.
This equation is part of trigonometric identities and can be useful in simplifying expressions or solving trigonometric equations.
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