| For any real value of \[\theta ,\]\[\sqrt{\frac{\sec \theta -1}{\sec \theta +1}}\]is equal to |
A) \[\cot \theta -\text{cosec}\theta \]
B) \[\sec \theta -\tan \theta \]
C) \[\text{cosec}\,\,\theta -\cot \theta \]
D) \[\tan \theta -\sec \theta \]
Correct Answer: C
Solution :
| \[\sqrt{\frac{\sec \theta -1}{\sec \theta +1}}=\sqrt{\frac{(\sec \theta -1)(sec\theta -1)}{(\sec \theta +1)(\sec \theta -1)}}\] |
| \[=\sqrt{\frac{{{(\sec \theta -1)}^{2}}}{{{\sec }^{2}}\theta -1}}=\sqrt{\frac{{{(\sec \theta -1)}^{2}}}{{{\tan }^{2}}\theta }}\] |
| \[=\frac{\sec \theta -1}{\tan \theta }=\text{cosec}\theta -\cot \theta \] |
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