A) 2
B) 3
C) 1
D) 0
Correct Answer: A
Solution :
\[\tan (90{}^\circ -\theta )=\cot \theta ,\ \cot (90{}^\circ -\theta )=\tan \theta .\] Therefore\[\frac{\cot 54{}^\circ }{\tan 36{}^\circ }+\frac{\tan 20{}^\circ }{\cot 70{}^\circ }\] \[=\frac{\cot 54{}^\circ }{\tan (90{}^\circ -54{}^\circ )}+\frac{\tan 20{}^\circ }{(\cot 90{}^\circ -20{}^\circ )}\] \[\frac{\cot 54{}^\circ }{\cot 54{}^\circ }+\frac{\tan 20{}^\circ }{\tan 20{}^\circ }=1+1=2\].
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