Trigonometric Identities Question 265
Question: If $ 2\sec 2\alpha =\tan \beta +\cot \beta , $ then one of the values of $ \alpha +\beta $ is
[Karnataka CET 2000]
Options:
A) $ \frac{\pi }{4} $
B) $ \frac{\pi }{2} $
C) $ \pi $
D) $ 2\pi $
Show Answer
Answer:
Correct Answer: A
Solution:
The given equation may be written as $ \frac{2}{\cos 2\alpha }=\frac{\sin \beta }{\cos \beta }+\frac{\cos \beta }{\sin \beta }=\frac{{{\sin }^{2}}\beta +{{\cos }^{2}}\beta }{\cos \beta \sin \beta } $ $ =\frac{1}{\cos \beta .\sin \beta } $
Þ $ \cos 2\alpha =\sin 2\beta $
Þ $ \cos 2\alpha $ = $ \cos ,( \frac{\pi }{2}-2\beta ) $
Þ $ 2\alpha =\frac{\pi }{2}-2\beta $
Þ
Þ .
BETA
