Question

Evaluate tan 1 tan 2 tan 3 . . . . Tan 89 = 1

Answer 1

HEY mate here is your answer.
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LHS
=tan 1 tan 2...tan 45 ....tan 88 tan 89
=tan 1 tan 2...tan 43 tan 44 tan 45 cot 44 cot 43...cot 2 cot 1
=tan 45
=1

hence LHS=RHS
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hope it helps you.

^_^

Answer 2

Hey there !!

Answer: 1 .

Step-by-step explanation:

= tan 1 . tan 2 . tan 3 ... tan 44 . tan 45 . tan 46 ... tan 87 . tan 88 . tan 89  

= tan 1 . tan 2 . tan 3 ... tan 44 . tan 45 . tan( 90 - 44 ) ... tan (90 - 3 ) . tan ( 90 - 2 ) . tan ( 90 - 1) 

= tan 1 . tan 2  . tan 3 ...tan44 . tan 45 . cot 44 ... cot 3 . cot 2 . cot 1 

= tan 1 . cot 1 . tan 2 . cot 2 . tan 3 . cot 3 ... tan 44 . cot 44 . tan 45 ... tan 89 . cot 89 

= 1 x 1 x 1 x ... 1 x ... x 1 . [ tan 45 = 1 ] .

= 1 .

Hence, it is solved .

THANKS

#BeBrainly .