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What is sec^-1⁡x in terms of tan^-1⁡?(a) tan^-1⁡\(\sqrt{1+x^2}\)(b) tan^-1⁡1+x^2(c) tan^-1⁡x(d) tan^-1⁡\(\sqrt{x^2-1}\)This question was posed to me by my college professor while I was bunking the class.My question comes from Properties of Inverse Trigonometric Functions topic in section Inverse Trigonometric Functions of Mathematics – Class 12

Answer» RIGHT OPTION is (d) tan^-1⁡\(\SQRT{x^2-1}\)

For EXPLANATION: LET sec^-1⁡x=y

⇒x=sec⁡y

⇒x=\(\sqrt{1+tan^2⁡y}\)

⇒x^2-1=tan^2⁡y

∴y=tan^-1⁡\(\sqrt{x^2-1}\)=sec^-1⁡x.


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