A) \[1\]
B) \[2\]
C) \[\sin \,\theta \]
D) \[\cos \,\theta \]
Correct Answer: A
Solution :
\[\frac{(\sin \theta +\cos \theta )\,(\tan \theta +\cot \theta )}{(\sec \theta +\cos ec\theta )}\] \[=\frac{(\sin \theta +\cos \theta )\left( \frac{\sin \theta }{\cos \theta }+\frac{\cos \theta }{\sin \theta } \right)}{\left( \frac{1}{\cos \theta }+\frac{1}{\sin \theta } \right)}\] \[=\frac{(\sin \theta +\cos \theta )\left( \frac{{{\sin }^{2}}\theta +{{\cos }^{2}}\theta }{\sin \theta \,\cos \theta } \right)}{\left( \frac{\sin \theta +\cos \theta }{\sin \theta \,\cos \theta } \right)}\] \[(\because \,\,\,\,{{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1)\] \[=\frac{\frac{\sin \theta +\cos \theta }{\sin \theta \,\cos \theta }}{\frac{\sin \theta +\cos \theta }{\sin \theta \,\cos \theta }}=\]
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