Find the Value of tan1.tan2.tan3……………..tan89

Answer: One. 

Explanation: To find the value of this question, we need to segregate the terms in a way that those values can be converted into cot because cot x= 1/tan x. 

(tan1…tan44) tan 45 [tan (90-44) tan (90-43)…. Tan (90-1)] 

Tan 1… tan 44 (1) (cot 44 cot 43…. Cot 1)

Since cot = 1/tan x, the equation becomes tan 1.tan2. ….. Tan44. 1/tan44. 1/tan 43… 1/tan1. 

All the terms will cancel out and the answer will be 1.