\(sin\left(cos^{-1}\frac{3}{5}\right)\)=?A. \(\frac{3}{4}\)B. \(\fra

1.	\(sin\left(cos^{-1}\frac{3}{5}\right)\)=?A. \(\frac{3}{4}\)B. \(\frac{4}{5}\)C. \(\frac{3}{5}\)D. none of these
Answer» Correct Answer is \(\frac{4}{5}\) Let, x = \(cos^{-1}\frac{3}{5}\) ⇒ cos x = \(\frac{3}{5}\) Now , sin(\(cos^{-1}\frac{3}{5}\)) becomes sin (x) Since we know that sin x =\(\sqrt{1-cos^2x}\) \(=\sqrt{1-(\frac{3}{5})^2}\) \(sin\left(cos^{-1}\frac{3}{5}\right)\)= Sin x= \(\frac{4}{5}\)

\(sin\left(cos^{-1}\frac{3}{5}\right)\)=?A. \(\frac{3}{4}\)B. \(\frac{4}{5}\)C. \(\frac{3}{5}\)D. none of these

Answer»

Correct Answer is \(\frac{4}{5}\)

Let, x = \(cos^{-1}\frac{3}{5}\)

⇒ cos x = \(\frac{3}{5}\)

Now , sin(\(cos^{-1}\frac{3}{5}\)) becomes sin (x)

Since we know that sin x =\(\sqrt{1-cos^2x}\)

\(=\sqrt{1-(\frac{3}{5})^2}\)

\(sin\left(cos^{-1}\frac{3}{5}\right)\)= Sin x= \(\frac{4}{5}\)