Trigonometric Equations Question 86
Question: If $ \tan (\pi \cos \theta )=\cot (\pi \sin \theta ), $ then the value of $ \cos ( \theta -\frac{\pi }{4} ) $ =
[UPSEAT 1999]
Options:
A) $ \frac{1}{2\sqrt{2}} $
B) $ \frac{1}{\sqrt{2}} $
C) $ \frac{1}{3\sqrt{2}} $
D) $ \frac{1}{4\sqrt{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} $
$ \Rightarrow ,\cos ( \theta -\frac{\pi }{4} )=\frac{1}{2\sqrt{2}} $ .
BETA
