Question

prove that thee value of tan1.tan2.tan3...........tan89=1

Answer 1

tan 1 . tan 2 . tan 3 ... tan 87 . tan 88 . tan 89 = LHS 

tan 1 . tan 2 . tan 3 ... tan (90 - 3 ) . tan ( 90 - 2 ) . tan ( 90 - 1) 

tan 1 . tan 2  . tan 3 ... cot 3 . cot 2 . cot 1 

tan 1 . cot 1 . tan 2 . cot 2 . tan 3 . cot 3 ... tan 89 . cot 89 

1 x 1 x 1 x 1 x ... x 1 

As 1ⁿ = 1  = RHS 

Where n = any positive integer 

Answer 2

Hey there !

tan1.tan2......tan45.....tan88.tan89

tan1.tan2....tan45...tan(90-2).tan(90-1)

tan1.tan2....tan45....cot2.cot1

We know that :- tanA.cotA=1

so ,1^44.tan45

= 1*1

=1

hope helped !