Q. The value of $\tan{1{^\circ}\tan{2{^\circ}\tan{3{^\circ}\ldots\tan{89{^\circ}}}}}$ is equal to
A) $- 1$
B) 2
C) $\frac{\pi}{2}$
D) 1
Explanation
(d)
$\tan{1{^\circ}\tan{2{^\circ}\tan{3{^\circ}\ldots\tan{89{^\circ}}}}}$
$= \tan{1{^\circ}\tan{2{^\circ}\tan{3{^\circ}\ldots tan\ 45{^\circ}\ cot\ 44{^\circ}\ldots cot\ 2{^\circ}\ cot\ 1{^\circ}}}}$
$= \left( \tan{1{^\circ}\cot{1{^\circ}}} \right)\left( \tan{2{^\circ}\cot{2{^\circ}}} \right)\ldots\tan{45{^\circ} = 1.1\ldots..1 = 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.