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