| If \[\sec \theta +\tan \theta =2,\] then what is the value of \[\sec \theta ?\] |
A) \[\frac{3}{2}\]
B) \[\sqrt{2}\]
C) \[\frac{5}{2}\]
D) \[\frac{5}{4}\]
Correct Answer: D
Solution :
| By trigonometric identity, |
| \[{{\sec }^{2}}\theta -{{\tan }^{2}}\theta =1\] |
| \[\Rightarrow \]\[(\sec \theta +\tan \theta )(\sec \theta -\tan \theta )=1\] |
| \[\Rightarrow \] \[\sec \theta -tan\theta =\frac{1}{2}\] (i) |
| and given, \[\sec \theta +\tan \theta =2\] ... (ii) |
| On adding Eqs. (i) and (ii), we get |
| \[2\sec \theta =\frac{1}{2}+2\] |
| \[\therefore \] \[\sec \theta =\frac{5}{4}\] |
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