The value of tan 25° tan 10° tan 80° tan 65° is __________.

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Solution

$\tan 25 ° \tan 10 ° \tan 80 ° \tan 65 ° = \tan 25 ° \tan 10 ° \tan (90 ° - 10 °) \tan (90 ° - 25 °) = \tan 25 ° \tan 10 ° \cot 10 ° \cot 25 ° [\tan (90 ° - θ) = \cot θ]$
$= \tan 25 ° \cot 25 ° \times \tan 10 ° \cot 10 ° = 1 \times 1 (\cot θ = \frac{1}{\tan θ}) = 1$

The value of tan 25° tan 10° tan 80° tan 65° is _1_.

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