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Which of the following formula is incorrect?(a) sin^-1⁡x+sin^-1⁡y=sin^-1⁡{\(x\sqrt{1-y^2}+y\sqrt{1-x^2}\)}(b) sin^-1⁡x-sin^-1⁡y=sin^-1⁡{\(x\sqrt{1+y^2}+y\sqrt{1+x^2}\)}(c) 2 tan^-1⁡x=tan^-1⁡\((\frac{2x}{1-x^2})\)(d) 2 cos^-1⁡x=cos^-1⁡(3x-4x^3)The question was posed to me in an interview.Question is taken from Properties of Inverse Trigonometric Functions in portion Inverse Trigonometric Functions of Mathematics – Class 12

Answer»

The correct answer is (B) sin^-1⁡x-sin^-1⁡y=sin^-1⁡{\(x\SQRT{1+y^2}+y\sqrt{1+x^2}\)}

EASY EXPLANATION: The formula sin^-1⁡x-sin^-1⁡y=sin^-1⁡{\(x\sqrt{1+y^2}+y\sqrt{1+x^2}\)} is incorrect. The correct formula is sin^-1⁡x-sin^-1⁡y=sin^-1⁡{\(x\sqrt{1+y^2}-y \sqrt{1-x^2}\)}.


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