Question : What is the value of $\tan 10°. \tan 25°. \tan 45°.\tan 65°. \tan 80°$
Option 1: $\sqrt{3}$
Option 2: $2$
Option 3: $0$
Option 4: $1$
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Correct Answer: $1$
Solution :
Given expression,
$\tan 10°. \tan 25°. \tan 45°.\tan 65°. \tan 80°$
We know, $\tan (90° - θ) = \cotθ$
$=\tan (90° - 80°) × \tan (90° - 65°) × \tan 45° × \tan 65° × \tan 80° $
$=\cot 80° × \cot 65° × 1 × \tan 65° × \tan 80°$
$=1$
Hence, the correct answer is $1$.
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