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Question:

Let tan y = tan x + tan(2x/(1 - x^2)) where |x| < 1/√3. Then a value of y is

3x+x³/1+3x²

3x+x³/√x²

3x−x³/1+3x²

3x−x³/√x²

Solution:

Let tan x = θ
2θ = tan(2x/(1 - x^2)) ⇒ tan(2x/(1 - x^2)) = 2θ
Then, tan y = tan x + 2 tan x
tan y = 3 tan x ⇒ tan y = 3 tan x
tan y = (3x - x³)/√x² ⇒ y = 3x - x³/√x²
Hence, option A is correct.