A) \[\frac{\sqrt{3}}{2}\]
B) \[0\]
C) \[\frac{1}{\sqrt{2}}\]
D) \[1\]
Correct Answer: D
Solution :
| [d] \[\cot \,41{}^\circ \cdot \cot \,42{}^\circ \cdot \cot \,43{}^\circ \cdot \cot \,44{}^\circ \cdot \cot \,45{}^\circ \] \[\cot \,46{}^\circ \cdot \cot \,47{}^\circ \cdot \cot 48{}^\circ \cdot \cot 49{}^\circ \] \[=\cot \,41{}^\circ \cdot \cot \,42{}^\circ .\cot 43{}^\circ \cdot \cot \,44{}^\circ \cdot \cot \,45{}^\circ \] \[\tan (90{}^\circ -46{}^\circ )\cdot tan(90{}^\circ -46{}^\circ ).\] \[\tan \,(90{}^\circ -48{}^\circ )\cdot \tan (90{}^\circ -49{}^\circ )\] \[=\cot 41{}^\circ \cdot \cot 42{}^\circ \cdot \cot 43\cdot \cot 44{}^\circ .\cot 45{}^\circ \cdot tan44{}^\circ \] \[\tan 43{}^\circ \cdot \tan 42{}^\circ \cdot \tan 41{}^\circ =\cot 45{}^\circ =1\] |
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