Complex Numbers And Quadratic Equations question 300
Question: $ \cosh (\alpha +i\beta )-\cosh (\alpha -i\beta ) $ is equal to [RPET 2000]
Options:
A) $ 2\sinh \alpha \sinh \beta $
B) $ 2\cosh \alpha \cosh \beta $
C) $ 2i\sinh \alpha \sin \beta $
D) $ 2\cosh \alpha \cos \beta $
Show Answer
Answer:
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 $ .
BETA
