A) 1
B) 2
C) 3
D) 4
Correct Answer: B
Solution :
\[\frac{\cos 70{}^\circ }{\sin 20{}^\circ }+\frac{cos\,55{}^\circ \cos ec\,35{}^\circ }{\tan 5{}^\circ \,\tan \,25{}^\circ \,\tan 45{}^\circ }\] \[\tan \,\,65{}^\circ \,\,\tan \,85{}^\circ \] \[=\frac{\cos (90{}^\circ -20{}^\circ )}{\sin 20{}^\circ }+\frac{\cos 55{}^\circ \cos ec(90{}^\circ -55{}^\circ )}{\tan 5{}^\circ \,\tan \,25{}^\circ \,\tan 45{}^\circ }\] \[tan\left( 90{}^\circ -25{}^\circ \right)tan\left( 90{}^\circ -\text{ }5{}^\circ \right)\] \[=\frac{\sin \,20{}^\circ }{sin\,20{}^\circ }+\frac{\cos 55{}^\circ \sec 55{}^\circ }{\tan 5{}^\circ \,\tan 25{}^\circ \,\tan 45{}^\circ \,\cot 25{}^\circ \,\cot 5{}^\circ }\] \[=1+\frac{1}{\tan 45{}^\circ }=1+1=2\] \[\left[ \because \,\tan \,\,5{}^\circ \,\cot 5{}^\circ =1\,\,and\,\,\tan \,25{}^\circ .cot\,25{}^\circ =1 \right]\]
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