If tan(x + y) tan(x - y) = 1, then find the value of tan x.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 1.
tan(x + y) tan(x - y) = 1
⇒ [(tan x + tan y)/(1 - tan x tan y)] × [(tan x - tan y)/(1 + tan x tan y)] = 1
⇒ (tan2x - tan2y)/(1 - tan2x tan2y) = 1
⇒ tan2x - tan2y = 1 - tan2x tan2y
⇒ tan2x + tan2x tan2y = 1 + tan2y
⇒ tan2x(1 + tan2y) = 1 + tan2y
⇒ tan2x = 1
⇒ tan x = 1
Therefore, the value of tan x is 1.