Complex Numbers And Quadratic Equations question 224
Question: The value of $ \frac{(\cos \alpha +i\sin \alpha )(\cos \beta +i\sin \beta )}{(\cos \gamma +i\sin \gamma )(\cos \delta +i\sin \delta )} $ is [RPET 2001]
Options:
A) $ \cos (\alpha +\beta -\gamma -\delta )-i\sin (\alpha +\beta -\gamma -\delta ) $
B) $ \cos (\alpha +\beta -\gamma -\delta )+i\sin (\alpha +\beta -\gamma -\delta ) $
C) $ \sin (\alpha +\beta -\gamma -\delta )-i\cos (\alpha +\beta -\gamma -\delta ) $
D) $ \sin (\alpha +\beta -\gamma -\delta )+i\cos (\alpha +\beta -\gamma -\delta ) $
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Answer:
Correct Answer: B
Solution:
$ \frac{(\cos \alpha +i\sin \alpha )(\cos \beta +i\sin \beta )}{(\cos \gamma +i\sin \gamma )(\cos \delta +i\sin \delta )} $ $ =\cos (\alpha +\beta -\gamma -\delta )+i\sin (\alpha +\beta -\gamma -\delta ) $ [By de-movire’s theorem].
BETA
