Question

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 1

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⁡{\(x\sqrt{1+y^2}-y \sqrt{1-x^2}\)}.