Question : The value of $\tan1° \tan2° \tan3°...\tan89°$ is:
Option 1: $1$
Option 2: $0$
Option 3: $\sqrt{3}$
Option 4: $\frac{1}{\sqrt{3}}$
Answer (1)
24th Jan, 2024
Correct Answer: $1$
Solution :
$\tan1° \tan2° \tan3°...\tan89°$
$= \tan1° \tan2° \tan3°...\tan45°...\tan(90-3)°\tan(90-2)°\tan(90-1)°$
$=\tan1° \tan2° \tan3°...\tan45°...\cot3°\cot2°\cot1°$
As we know, $\tan\theta=\frac{1}{\cot\theta}$
So, it will cancel out all the terms except $\tan45°$.
$=\tan45°$
$= 1$
Hence, the correct answer is $1$.
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