Quantitative Aptitude Ques 2485
Question: If $ 2\sin \theta =\sec \theta , $ what is the value of $ {{\sin }^{4}}\theta +{{\cos }^{4}}\theta ? $
Options:
A) 1
B) $ \frac{1}{2} $
C) $ \frac{1}{4} $
D) $ \frac{1}{8} $
Show Answer
Answer:
Correct Answer: B
Solution:
- $ 2\sin \theta =\sec \theta $
$ \Rightarrow $ $ 2\sin \theta \cos \theta =1 $
$ \Rightarrow $ $ \sin 2\theta =1 $
$ \Rightarrow $ $ \sin 2\theta =sin90{}^\circ $
$ \Rightarrow $ $ 2\theta =90{}^\circ $
$ \Rightarrow $ $ \theta =45{}^\circ $
$ \therefore $ $ {{\sin }^{4}}\theta +{{\cos }^{4}}\theta ={{( \frac{1}{\sqrt{2}} )}^{4}}+{{( \frac{1}{\sqrt{2}} )}^{4}}=\frac{1}{2} $
BETA
