A) 2
B) 3
C) \[-2\]
D) 1
Correct Answer: A
Solution :
We have, \[1+{{\cot }^{2}}\theta ={{(\sqrt{3+2\sqrt{2}}-1)}^{2}}\] \[\cos e{{c}^{2}}\theta ={{(\sqrt{2+1+2\sqrt{2}}-1)}^{2}}\] \[={{\left( \sqrt{{{(\sqrt{2}+1)}^{2}}}-1 \right)}^{2}}={{(\sqrt{2}+1-1)}^{2}}={{(\sqrt{2})}^{2}}\] \[\Rightarrow \] \[\cos ec\,\theta =2\] \[\sin \theta =\frac{1}{2},\cos \theta =\frac{\sqrt{3}}{2},\tan \theta =\frac{1}{\sqrt{3}}\] Now, \[\frac{1}{\tan \theta }+\frac{\sin \theta }{1+\cos \theta }=\sqrt{3}+\frac{1/2}{1+\sqrt{3}/2}=2\]
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