1.

What is the value of 2 tan^-1⁡x in terms of sin^-1⁡?(a) sec^-1⁡x(b) 2 sec^-1⁡x(c) 2 sec^-1⁡\((\sqrt{1+x^2})\)(d) sec^-1⁡\((\sqrt{1+x^2})\)This question was posed to me during an internship interview.My question is based upon Properties of Inverse Trigonometric Functions topic in portion Inverse Trigonometric Functions of Mathematics – Class 12

Answer»

The correct OPTION is (C) 2 sec^-1⁡\((\sqrt{1+x^2})\)

The EXPLANATION: Let 2 tan^-1⁡x=y

⇒tan^-1⁡x=\(\frac{y}{2}\)

From ∆ABC, we get

⇒tan^-1⁡x=sec^-1⁡\(\sqrt{1+x^2}=\frac{y}{2}\)

⇒y=2 sec^-1⁡(\(\sqrt{1+x^2}\))


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