| If \[(\cos \theta +\sec \theta )=2,\]then \[({{\cos }^{2}}\theta +{{\sec }^{2}}\theta )\] is equal to |
A) \[\frac{1}{2}\]
B) 2
C) 4
D) \[\frac{1}{4}\]
Correct Answer: B
Solution :
| \[\cos \theta +\sec \theta =2\] |
| \[{{(\cos \theta +\sec \theta )}^{2}}={{(2)}^{2}}\][squaring on both sides] |
| \[{{\cos }^{2}}\theta +{{\sec }^{2}}\theta +2\cos \theta \times \sec \theta =4\] |
| \[\Rightarrow \] \[{{\cos }^{2}}\theta +{{\sec }^{2}}\theta +2=4\] |
| \[\Rightarrow \] \[{{\cos }^{2}}\theta +{{\sec }^{2}}\theta =4-2\] |
| \[\Rightarrow \] \[{{\cos }^{2}}\theta +{{\sec }^{2}}\theta =2\] |
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