Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-1

If \[(\cos \theta +\sec \theta )=\frac{5}{2},\] then \[({{\cos }^{2}}\theta +{{\sec }^{2}}\theta )\] is equal to

A) \[\frac{33}{4}\]

B) \[\frac{21}{4}\]

C) \[\frac{29}{4}\]

D) \[\frac{17}{4}\]

Correct Answer: D

Solution :

[d] \[{{(\cos \theta +sec\theta )}^{2}}=\frac{25}{4}\]

\[\Rightarrow \]\[{{\cos }^{2}}\theta +{{\sec }^{2}}\theta +2\cos \theta \sec \theta =\frac{25}{4}\]

\[\Rightarrow \] \[{{\cos }^{2}}\theta +{{\sec }^{2}}\theta +2=\frac{25}{4}\]

\[\Rightarrow \] \[({{\cos }^{2}}\theta +{{\sec }^{2}}\theta )=\left[ \frac{25}{4}-2 \right]=\frac{17}{4}\]