A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{2}\]
C) \[\pi \]
D) \[0\]
Correct Answer: A
Solution :
| We have, \[x\,\tan \alpha +y\sec \alpha =1\] |
| \[\frac{x}{\cot \alpha }+\frac{y}{\cos \alpha }=1\] |
| Intercept are cot\[\alpha \] and cos \[\alpha \]. Given, \[\cot \alpha .\cos \alpha =\sin \alpha \] |
| \[{{\tan }^{2}}\alpha =1\] \[\Rightarrow \,\,\,\,\,\tan \alpha =\pm 1\] |
| \[\alpha =\pm \frac{\pi }{4}\Rightarrow \alpha =\frac{\pi }{4}\] |
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