Quantitative Aptitude Ques 509
Question: If $ (\cos \theta +\sec \theta )=\frac{5}{2}, $ then $ ({{\cos }^{2}}\theta +{{\sec }^{2}}\theta ) $ is equal to
Options:
A) $ \frac{33}{4} $
B) $ \frac{21}{4} $
C) $ \frac{29}{4} $
D) $ \frac{17}{4} $
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] $ {{(\cos \theta +sec\theta )}^{2}}=\frac{25}{4} $
$ \Rightarrow $ $ {{\cos }^{2}}\theta +{{\sec }^{2}}\theta +2\cos \theta \sec \theta =\frac{25}{4} $
$ \Rightarrow $ $ {{\cos }^{2}}\theta +{{\sec }^{2}}\theta +2=\frac{25}{4} $
$ \Rightarrow $ $ ({{\cos }^{2}}\theta +{{\sec }^{2}}\theta )=[ \frac{25}{4}-2 ]=\frac{17}{4} $
BETA
