Question : The value of tan 25° tan 35° tan 45° tan 55° tan 65° is:
Option 1: $2$
Option 2: $1$
Option 3: $\sqrt{3}$
Option 4: $0$
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Correct Answer: $1$
Solution :
The trigonometric identity $\tan A.\cot A = 1$ and $\tan (90° -\theta) = \cot \theta$
$\tan 25° \tan 35° \tan 45° \tan 55° \tan 65°$
$ = \tan 25°×\tan 35° \times 1\times \tan(90° - 35°)×\tan(90° - 25°)$
$ = \tan 25° ×\tan 35° \times 1\times \cot 35°× \cot 25°$
$ = 1$
Hence, the correct answer is 1.
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