Question

Find the value of tan1°tan2°tan3°......tan89°

Answer 1

tan1.tan2.........tan89
but tan 89 can be written as cot 1[tan(90-1)=cot 1] by tan(90-theta)=cot(theta)
likewise......,
tan 88 =cot 2
tan 87= cot 3
................up to tan 46=cot 44
then middle one is tan 45 =1
so it is 
tan1.tan2...........tan44.tan 45.cot44..............cot1
tan and cot cancel out by[tan (theta)*cot(theta)=1
so ....remaining is 1
answer =1

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 .