| What is the value of \[(90{}^\circ -\theta )\cdot \sin \theta \sec 45{}^\circ ?\] |
A) \[1\]
B) \[\frac{\sqrt{3}}{2}\]
C) \[\sqrt{2}\]
D) \[\sqrt{3}\]
Correct Answer: C
Solution :
| Given, \[\sec \,\,(90-\theta ){}^\circ sin\theta sec45{}^\circ \] |
| \[=\text{cosec}\,\,\theta \sin \theta \sec 45{}^\circ \] |
| \[=\frac{1}{\sin \theta }\cdot \sin \cdot (\sqrt{2})=\sqrt{2}\] |
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