| What is \[\sqrt{\frac{1+\sin \theta }{1-\sin \theta }}\] equal to? |
A) \[\sec \theta -\tan \theta \]
B) \[\sec \theta +\tan \theta \]
C) \[\cos ec\theta +\cot \theta \]
D) \[\cos ec\theta -\cot \theta \]
Correct Answer: B
Solution :
| \[\sqrt{\frac{1+\sin \theta }{1-\sin \theta }}\] |
| On multiplying with \[1+\sin \theta \] in numerator and denominator, we get |
| \[\sqrt{\frac{(1+\sin \theta )}{(1-\sin \theta )}\times \frac{(1+\sin \theta )}{(1+\sin \theta )}}\] |
| \[=\,\,\sqrt{\frac{{{(1+\sin \theta )}^{2}}}{1-{{\sin }^{2}}\theta }}=\sqrt{\frac{{{(1+\sin \theta )}^{2}}}{{{\cos }^{2}}\theta }}\] |
| \[\Rightarrow \] \[\frac{1+\sin \theta }{\cos \theta }=\frac{1}{\cos \theta }+\frac{\sin \theta }{\cos \theta }\] |
| \[=\sec \theta +\tan \theta \] |
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