Trigonometric Identities Question 169
Question: If $ \cos (\alpha -\beta )=1 $ and $ \cos (\alpha +\beta )=\frac{1}{e} $ , $ -\pi <\alpha ,\beta <\pi $ , then total number of ordered pair of $ (\alpha ,\beta ) $ is
[IIT Screening 2005]
Options:
A) 0
B) 1
C) 2
D) 4
Show Answer
Answer:
Correct Answer: D
Solution:
$ -2\pi <\alpha -\beta <2\pi $ $ \cos (\alpha -\beta )=1 $ Þ $ \alpha -\beta =0 $ Þ $ \alpha =\beta $ $ \cos 2\alpha =\frac{1}{e} $ and $ -2\pi <2\alpha <2\pi $ Hence, there will be four solutions.
BETA
