Trigonometric Equations Question 88
Question: If $ \tan (\pi \cos \theta )=\cot (\pi \sin \theta ) $ , then $ \sin ( \theta +\frac{\pi }{4} ) $ equals
[AMU 1999]
Options:
A) $ \frac{1}{\sqrt{2}} $
B) $ \frac{1}{2} $
C) $ \frac{1}{2\sqrt{2}} $
D) $ \frac{\sqrt{3}}{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ \tan (\pi \cos \theta )=\tan ( \frac{\pi }{2}-\pi \sin \theta ) $
$ \therefore \sin \theta +\cos \theta =\frac{1}{2} $
Þ $ \sin ( \theta +\frac{\pi }{4} )=\frac{1}{2\sqrt{2}} $ .
BETA
