Question

Prove the property is you can ???

Answer 1

Heya!!
Let tan-¹(x) = ∅ => x = tan∅
We know that tan2∅ = 2Tan∅/1-tan²∅
=> Tan2∅ = 2x/1-x²

Now -1≤x≤1 => -1≤tan∅≤1
=> -π/2≤2∅≤π/2
tan2∅ = 2x/1-x² => 2∅=tan-¹(2x/1-x²)
Hence 2tan-¹(2x/1-x²) where -1≤x≤1 .