Question

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

Answer 1

LHS= tan1.tan2.tan3.............tan87.tan88.tan89
=tan1.tan2.tan3.............tan(90-3)tan(90-2)tan(90-1)
=tan1.tan2.tan3............cot3.cot2cot1
=tan1.cot1.tan2.cot2.tan3.cot3.............
=1.1.1....... since tan.cot=1
=1
=RHS

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 .