Aptitude Question ID : 94428

The value of \tan 4^{\circ}\cdot \tan 43^{\circ}\cdot \tan 47^{\circ}\cdot \tan 86^{\circ} is :
[A]1
[B]2
[C]3
[D]4

1
Given Expression, \tan 4^{\circ}\cdot \tan 43^{\circ}\cdot \tan 47^{\circ}\cdot \tan 86^{\circ}
= \tan 4^{\circ}\cdot \tan 43^{\circ}\cdot \tan (90^{\circ}-43^{\circ})\cdot \tan (90^{\circ}-4^{\circ})
= \tan 4^{\circ}\times \tan 43^{\circ}\times \cot 43^{\circ}\times \cot 4^{\circ} = 1
\left [\because  \tan \left ( 90^{\circ} - \theta \right ) = \cot \theta; \tan \theta\cdot \cot \theta = 1 \right ]
Hence option [A] is correct answer.

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