Question

$Sin\left(co{s}^{-1}\frac{3}{5}\right)+sin(\frac{\pi }{2}-si{n}^{-1}(-\frac{\sqrt{3}}{2}))=$

• A. $\frac{13}{10}$
• B. $\frac{8+5\sqrt{3}}{10}$
• C. $\frac{3}{10}$
• D. None

Answer 1

The correct option is A $\frac{13}{10}$

$sinco{s}^{-1}\left(\frac{3}{5}\right)=sin\left(si{n}^{-1}\frac{4}{5}\right)=\frac{4}{5}sin(\frac{\pi }{2}-si{n}^{-1}(-\frac{\sqrt{3}}{2}\left)\right)=sin(\frac{\pi }{2}+\frac{\pi }{3})=sin\frac{5\pi }{6}=\frac{1}{2}\therefore L.H.S.=\frac{4}{3}+\frac{1}{2}=\frac{13}{10}$.