Question

$ \cos (\alpha +i\beta ) $ is equal to

• A. $ cos\text{ }\alpha \text{ }coch\text{ }\beta -2\text{ }sin\text{ }\alpha \text{ }sinh\text{ }\beta $
• B. $ cos\text{ }\alpha \text{ }cosh\text{ }\beta +2\text{ }sin\text{ }\alpha \text{ }sinh\text{ }\beta $
• C. $ cosh\text{ }\alpha \text{ }cos\text{ }\beta -2\text{ }sinh\text{ }\alpha \text{ }sin\text{ }\beta $
• D. None of the above

Answer 1

Answer: (A)

$ \cos (\alpha +i\beta )=\cos \alpha \cos i\beta -\sin \alpha \sin i\beta $ $ =\cos \alpha \cosh \beta -i\sin \alpha \sinh \beta $