Trigonometric Equations Question 281
Question: If $ 5{{\cos }^{2}}\theta +7{{\sin }^{2}}\theta -6=0 $ , then the general value of $ \theta $ is
Options:
A) $ 2n\pi \pm \frac{\pi }{4} $
B) $ n\pi \pm \frac{\pi }{4} $
C) $ n\pi +{{(-1)}^{n}}\frac{\pi }{4} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- $ 5-5{{\sin }^{2}}\theta +7{{\sin }^{2}}\theta =6 $
$ \Rightarrow $ $ 2{{\sin }^{2}}\theta =1 $
$ \Rightarrow $ $ {{\sin }^{2}}\theta =\frac{1}{2}={{\sin }^{2}}( \frac{\pi }{4} )\Rightarrow \theta =n\pi \pm \frac{\pi }{4} $ .
BETA
