A) \[2\,\,\sinh \,\alpha \,\,\sinh \,\beta \]
B) \[2\,\,\cosh \,\alpha \,\,\cosh \,\beta \]
C) \[2i\,\,\sinh \,\alpha \,\,\sin \,\beta \]
D) \[2\,\,\cosh \,\alpha \,\,\cos \,\beta \]
Correct Answer: C
Solution :
\[\cosh (\alpha +i\beta )-\cosh (\alpha -i\beta )\] = \[\cosh \,\alpha \cosh \,(i\beta )+\sinh \alpha \sinh (i\beta )\]\[-\cosh \alpha \,\cosh \,(i\beta )\,+\sinh \alpha \,\sinh \,(i\beta )\] \[=\,2\sinh \alpha \,\,\sinh \,i\beta \]\[=2i\,\sinh \alpha \,\sin \beta \].
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