Evaluate: cos(sin^-1 (4/5) + sin^-1 (12/13))

Question

Evaluate: cos(sin^-1 (\(\frac{4}{5}\)) + sin^-1 (\(\frac{12}{13}\)))

Answer 1

Let sin^-1 (\(\frac{4}{5}\)) = A 

sin A = \(\frac{4}{5}\)

∴ cos A = \(\frac{3}{5}\)

Let sin^-1 (\(\frac{12}{13}\)) = B 

\(\frac{12}{13}\) = sin B

sin B = \(\frac{12}{13}\)

∴ cos B = \(\frac{5}{13}\)

Now cos(sin^-1(\(\frac{4}{5}\)) + sin^-1 (\(\frac{12}{13}\))) = cos (A + B) 

= cos A cos B – sin A sin B