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Question
Prove that:
2 tan-1 (x) = `sin^-1 ((2x)/(1 + x^2))`
Solution
Let tan-1 x = θ
x = tan θ
sin 2θ = `(2 tan θ)/(1 + tan^2 θ) = "2x"/(1 + x^2)`
2θ = `sin^-1 ("2x"/(1 + x^2))`
∴ 2 tan-1 x = `sin^-1 ("2x"/(1 + x^2))` = RHS
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