A) 1
B) \[-1\]
C) 2
D) \[-2\]
Correct Answer: A
Solution :
\[x=\frac{\sin \theta \cos \left( 90{}^\circ -\theta \right)+\cos \theta \sin \left( 90{}^\circ -\theta \right)}{\tan \theta \sec \theta \left( 90{}^\circ -\theta \right)\sin \left( 90{}^\circ -\theta \right)}\] \[=\frac{\sin \theta sin\theta +\cos \theta \cos \theta }{\tan \theta \cos \theta .\operatorname{cosec}\theta }=\frac{{{\sin }^{2}}\theta +{{\cos }^{2}}\theta }{\frac{\sin \theta }{\cos \theta }\cdot \cos \theta \cdot \frac{1}{\sin \theta }}\] \[=\frac{1}{\frac{\sin \theta \cos \theta }{\sin \theta \cos \theta }}=1\]
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