\(sin[2tan^{-1}\frac{5}{8}]\) = ?A. \(\frac{25}{64}\)B. \(\frac{80}{

1.	\(sin[2tan^{-1}\frac{5}{8}]\) = ?A. \(\frac{25}{64}\)B. \(\frac{80}{89}\)C. \(\frac{75}{128}\)D. none of these
Answer» Correct Answer is (B) \(\frac{80}{89}\) Let, x = \(sin(2tan^{-1}\frac{5}{8})\) We know that 2 tan^-1x= sin^-1\((\frac{2x}{1+x^2})\) ⇒ x = sin\((sin^{-1}(\frac{2(\frac{5}{8})}{1+(\frac{5}{8})2})\)= sin(sin^-1(\(\frac{80}{89}\)))= \(\frac{80}{89}\)

\(sin[2tan^{-1}\frac{5}{8}]\) = ?A. \(\frac{25}{64}\)B. \(\frac{80}{89}\)C. \(\frac{75}{128}\)D. none of these

Answer»

Correct Answer is (B) \(\frac{80}{89}\)

Let, x = \(sin(2tan^{-1}\frac{5}{8})\)

We know that 2 tan^-1x= sin^-1\((\frac{2x}{1+x^2})\)

⇒ x = sin\((sin^{-1}(\frac{2(\frac{5}{8})}{1+(\frac{5}{8})2})\)= sin(sin^-1(\(\frac{80}{89}\)))= \(\frac{80}{89}\)