Trigonometric Identities Question 206
Question: If $ 2| \sin 2\alpha |=| \tan \beta +\cot \beta |,\alpha ,\beta \in ( \frac{\pi }{2},\pi ) $ ,then the value of $ \alpha +\beta $ is
Options:
A) $ \frac{3\pi }{4} $
B) $ \pi $
C) $ \frac{3\pi }{2} $
D) $ \frac{5\pi }{4} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ 2| \sin 2\alpha |\le 2 $ And $ | \tan \beta +\cot \beta |=\frac{1}{\sin \beta \cos \beta }=2\cos ec2\beta \ge 2 $
$ \therefore ,2| \sin 2\alpha |=| \tan \beta +\cot \beta |=2 $
$ \therefore ,\alpha =\beta =\frac{3\pi }{4} $
BETA
