A) 1
B) -1
C) 2
D) -2
Correct Answer: A
Solution :
\[cot\,\,5{}^\circ \text{ }cot\,\,10{}^\circ .........\text{ }cot\text{ }85{}^\circ \] \[=cot\,\,5{}^\circ \text{ }cot\,\,10{}^\circ .........cot(90{}^\circ -10{}^\circ )\cot (90{}^\circ -5{}^\circ )\] \[=cot\,\,5{}^\circ \text{ }cot\,\,10{}^\circ .........tan10{}^\circ \,\,tan5{}^\circ \] \[=(\tan 5{}^\circ \,\cot 5{}^\circ )\,\,(\tan 10{}^\circ \,\,\cot 10{}^\circ )\]??. \[=(1)(1)(1).......=1\]
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