A) 0
B) 1
C) \[\frac{1}{\sqrt{2}}\]
D) \[\frac{\sqrt{3}}{2}\]
Correct Answer: B
Solution :
| [b] \[\cot 41{}^\circ \cdot \cot 42{}^\circ \cdot \cot 43{}^\circ \cdot \cot 44{}^\circ \] |
| \[\cdot \cot 45{}^\circ \cdot \cot 46{}^\circ \cdot \cot 47{}^\circ \cdot \cot 48{}^\circ \cdot \cot 49{}^\circ \] |
| \[=\cot (90{}^\circ -49{}^\circ )\cdot \cot (90{}^\circ -48{}^\circ )\cdot \cot (90{}^\circ -47{}^\circ )\] |
| \[\cdot \cot (90{}^\circ -46{}^\circ )\cdot \cot 45{}^\circ -\cot 46{}^\circ \] |
| \[\cdot \cot 47{}^\circ \cdot \cot 48{}^\circ \cdot \cot 49{}^\circ \] |
| \[=\tan 49{}^\circ \cdot \tan 48{}^\circ \cdot \tan 47{}^\circ \cdot \tan 46{}^\circ \cdot \cot 45{}^\circ \] |
| \[\cdot \cot 46{}^\circ \cdot \cot 47{}^\circ \cdot \cot 48{}^\circ \cdot \cot 49{}^\circ \] |
| \[=1\cdot 1\cdot 1\cdot 1\cdot 1=1\] \[[\because \cot 45{}^\circ =1\,and\,\tan \theta \cdot \cot \theta =1]\] |
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