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
Correct Answer: A
Solution :
\[\cos (\alpha +i\beta )=\cos \alpha \cos i\beta -\sin \alpha \sin i\beta \] \[=\cos \alpha \cosh \beta -i\sin \alpha \sinh \beta \]
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