Question

Solve:
$\tan 5^o.\tan {15}^o.\tan {45}^o.\tan {75}^o.tan{85}^o$

Answer 1

$\tan 5°\cdot \tan 15°\cdot \tan 45°\cdot \tan 75°\cdot \tan 85°$

$=(\tan 5°\cdot \tan 85°)\cdot (\tan 15°\cdot \tan 75°)\cdot \tan 45°$

$=(\tan 5°\cdot \tan (90°-5°))\cdot (\tan 15°\cdot \tan (90°-15°))\cdot \tan 45°$

$=(\tan 5°\cdot \cot 5°)\cdot (\tan 15°\cdot \cot 15°)\cdot \tan 45°$

$=1\times 1\times 1=1$