Prove the Property if you can ?!
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Heya!!
Let tan-¹x = ∅ => x = tan∅
we know that sin2∅ = 2tan∅/1+tan²∅
=> sin2∅ = 2x/1+x²
Now -1≤x≤1 => -1≤tan∅≤1
=> -π/4 ≤∅≤π/4 => -π/2≤2∅≤π/2
So..
sin2∅ = 2x/1+x²
=> 2∅ = sin-¹(2x/1+X2) { 2∅ €[-π/2,π/2]
Hence 2Tan-¹x = sin-¹(2x/1+x²) Where -1≤x≤1
Let tan-¹x = ∅ => x = tan∅
we know that sin2∅ = 2tan∅/1+tan²∅
=> sin2∅ = 2x/1+x²
Now -1≤x≤1 => -1≤tan∅≤1
=> -π/4 ≤∅≤π/4 => -π/2≤2∅≤π/2
So..
sin2∅ = 2x/1+x²
=> 2∅ = sin-¹(2x/1+X2) { 2∅ €[-π/2,π/2]
Hence 2Tan-¹x = sin-¹(2x/1+x²) Where -1≤x≤1
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