Question

${\cos }^{-1}\frac{4}{5}+{\sin }^{-1}\frac{8}{17}$

• A. ${\cos }^{-1}\frac{77}{85}$
• B. ${\sin }^{-1}\frac{77}{85}$
• C. $\frac{\pi }{4}$
• D. None of these

Answer 1

The correct option is B ${\sin }^{-1}\frac{77}{85}$

Formula used :

$si{n}^{-1}x+si{n}^{-1}y=sin-1[x\sqrt{(1-y2)}+y\sqrt{(1-x2)}]$

Solution:

${\cos }^{-1}\frac{4}{5}+{\sin }^{-1}\frac{3}{5}$

${\sin }^{-1}\frac{3}{5}+{\sin }^{-1}\frac{8}{17}$

${\sin }^{-1}\{\frac{3}{5}\sqrt{1-{\left(\frac{8}{17}\right)}^2}+\frac{8}{17}\sqrt{1-{\left(\frac{3}{5}\right)}^2}\}$

${\sin }^{-1}\{\frac{3}{5}\times \frac{15}{17}+\frac{8}{17}\times \frac{4}{5}\}$

${\sin }^{-1}\left\{\frac{45+32}{85}\right\}={\sin }^{-1}\frac{77}{85}$