Trigonometric Equations Question 70
Question: The most general value of $ \theta $ satisfying the equations $ \tan \theta =-1 $ and $ \cos \theta =\frac{1}{\sqrt{2}} $ is
[MNR 1982; Roorkee 1990; UPSEAT 2002; MP PET 2003]
Options:
A) $ n\pi +\frac{7\pi }{4} $
B) $ n\pi +{{(-1)}^{n}}\frac{7\pi }{4} $
C) $ 2n\pi +\frac{7\pi }{4} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- $ \tan \theta =-1=\tan ( 2\pi -\frac{\pi }{4} ) $ , $ \cos \theta =\frac{1}{\sqrt{2}}=\cos ( 2\pi -\frac{\pi }{4} ) $ Hence general value is $ 2n\pi +( 2\pi -\frac{\pi }{4} )=2n\pi +\frac{7\pi }{4} $ .
BETA
