Question

$\tan 35°\tan 40°\tan 45°\tan 50°\tan 55°$

Answer 1

Find the value of the given expression

$\tan 35°\tan 40°\tan 45°\tan 50°\tan 55°$

$=\tan 35°\tan 40°\times 1\times \tan (90°-40°)\times \tan (90°-35°)$

$=\tan 35°\tan 40°\times 1\times cot40°\times cot35°$

$=\tan 35°\tan 40°\times 1\times \frac{1}{\tan 40°}\times \frac{1}{\tan 35°}$

$=1$