Question

Without using trigonometric tables prove that : tan 1° x tan 11° x tan 21° x tan 69° x tan 79° x tan 89° = 1

Answer 1

We know that
$\cot( \alpha ) \times \tan( \alpha ) = 1$

$\tan(90 - 89) \times \tan(90 - 79) \: \times \tan(90 - 69) \times \tan(69) \times \tan(79) \times \tan(89)$
We get,

$\cot(89) \times \cot(79) \times \cot(69) \times \tan(69) \times \tan(79) \times \tan(89) = 1$

Hope it helps.

Yours Truly
Yumieo