Question

tan10tan20tan70tan80

Answer 1

tan10tan20tan70tan80
=tan10tan80tan20tan70
=tan10cot(90-10)tan20cot(90-20)
=tan10cot10tan20cot20
=1

Answer 2

$\tan(10 ) \times \tan(20) \times \tan(70) \times \tan(80) = \\ \tan(90 - 80) \times \tan(90 - 70) \times \tan(70) \times \tan(80) = \\ because \tan(90 - \alpha ) = \cot( \alpha ) \\ \cot(80) \times \cot(70) \times \tan(70) \times \tan(80) = \\ 1 \times 1 = \\ 1$