A) 1
B) \[\sqrt{2}\]
C) 2
D) \[\sqrt{3}\]
Correct Answer: A
Solution :
sin\[\theta \] + cos\[\theta \] = \[\sqrt{3}\] On squaring both sides, we get (sin\[\theta \] + cos\[\theta \])2 = (\[\sqrt{3}\])2 \[\Rightarrow \] Sin2\[\theta \] + cos2\[\theta \] + 2sin\[\theta \]cos\[\theta \] = 3 \[\Rightarrow \] 1 + 2 sin \[\theta \] cos \[\theta \] = 3 \[\Rightarrow \] sin\[\theta \] cos\[\theta \]=\[\frac{3-1}{2}=\frac{2}{2}=1\] ?..(i) Now, tan \[\theta \] + cot \[\theta \] = \[\frac{\sin \theta }{\cos \theta }+\frac{\cos \theta }{\sin \theta }\] = \[\frac{{{\sin }^{2}}\theta +{{\cos }^{2}}\theta }{\sin \theta \cos \theta }=\frac{1}{\sin \theta \cos \theta }\] From Eq. (i), tan \[\theta \] + cos \[\theta \] = \[\frac{1}{1}=\mathbf{1}\]
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