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