Question

Tan 1° tan 2°tan3° ....tan 89°=1
Proove that

Answer 1

tan1° tan2° tan3°.....tan89°

tan1° tan2° tan3°.....tan(90 - 2)° tan(90-1)°

tan1° tan2° tan3° .....cot2° cot1°

We know that tan1° x cot1° = 1

tan1° x cot1° tan2° x cot°2 tan°3 x cot°3.....
= 1

Hence Proved

Hope This Helps You!

Answer 2

tan 89°
= tan (90-1)°
= cot 1°

similarly
tan 88° = cot2° and so on

therefore

tan 89° tan 88° tan 87° .... tan 46 °
= cot 1° cot 2° cot 3° .... cot 44°

now

LHS
= Tan 1° tan 2°tan3° ....tan 89
= Tan 1° tan 2°tan3° ....tan 44°tan 45° cot 44° ... cot 1°
= tan 45°
(tan and cot gets cancelled)
= 1
= RHS
(proved )