Question

what is the value of expression
tan0.tan1.tan2.tan3.........tan90 ??

Answer 1

Tan1.tan2......tan89
But tan can be written as cot 1 [tan{90-1}=cot1] by tan (90-theta)=cot(theta)
Likewise...........,
Tan88=cot2
Tan87=cot3
......up to tan46=cot44 then middle one is tan45=1
So it is tan1. tan....... Tan44.tan45.cot 44....cot tan and cot cancel out by [tan(theta)*cot(theta)=1] so ....remaining is 1

Answer is 1 ...!!

Answer 2

Hey there !!

Answer: 1 .

Step-by-step explanation:

= tan 0 . tan 1 . tan 2 . tan 3 ... tan 44 . tan 45 . tan 46 ... tan 87 . tan 88 . tan 89 . tan 90

= tan 0 . tan 1 . tan 2 . tan 3 ... tan 44 . tan 45 . tan( 90 - 44 ) ... tan (90 - 3 ) . tan ( 90 - 2 ) . tan ( 90 - 1) . tan ( 90 - 0 ) .

= tan 0 . tan 1 . tan 2  . tan 3 ...tan44 . tan 45 . cot 44 ... cot 3 . cot 2 . cot 1 . cot 0.

= tan 0. cot 0. 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 .