Aptitude Question ID : 94439
The value of $latex \tan 1^{\circ}\tan 2^{\circ}\tan 3^{\circ}……..\tan 89^{\circ}$ is :
[A]$latex 0$
[B]$latex 1$
[C]$latex \sqrt{3}$
[D]$latex \frac{1}{\sqrt{3}}&s=1$
$latex \mathbf{1}$
$latex \tan 1^{\circ}\tan 2^{\circ}\tan 3^{\circ}……..\tan 89^{\circ}$
$latex = \left ( \tan 1^{\circ}\cdot \tan 89^{\circ} \right )\cdot \left ( \tan 2^{\circ}\cdot \tan 88^{\circ} \right )……..\tan 45^{\circ}$
$latex = \left ( \tan 1^{\circ}\cdot \cot 1^{\circ} \right )\cdot \left ( \tan 2^{\circ}\cdot \cot 2^{\circ} \right )……..\tan 45^{\circ} = 1$
$latex \left [\because \tan \left ( 90^{\circ} – \theta \right ) = \cot \theta; \tan \theta\cdot \cot \theta = 1 \right ]$
Hence option [B] is correct answer.