Question:
If tanxtany=a and x+ y=30, then tanx and tany satisfy the equation
Answer:
Given, tan x * tan y = a and x + y = 30°
Now, tan(x + y) = tan 30°
=> (tan x + tan y)/(1 - tan x * tan y) = 1/√3
=> (tan x + tan y)/(1 - a) = 1/√3
=> (tan x + tan y)/(1 - a) = (1 * √3)/(√3 * √3)
=> (tan x + tan y)/(1 - a) = √3/3
=> tan x + tan y = √3(1 - a)/3
This is the required relation between tan x and tan y
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