Question

If ${\cos }^{-1}\frac{3}{5}+{\cos }^{-1}\frac{12}{13}={\cos }^{-1}k,$ then the value of $k$ is

• A. $\frac{16}{65}$
• B. $\frac{12}{65}$
• C. $\frac{11}{65}$
• D. $\frac{19}{65}$

Answer 1

The correct option is A $\frac{16}{65}$

${\cos }^{-1}\frac{3}{5}+{\cos }^{-1}\frac{12}{13}={\cos }^{-1}k,$

Applying $\cos$ both the sides

$\Rightarrow \cos \left({\cos }^{-1}\frac{3}{5}\right)\cos \left({\cos }^{-1}\frac{12}{13}\right)-\sin \left({\cos }^{-1}\frac{3}{5}\right)\sin \left({\cos }^{-1}\frac{12}{13}\right)=k\Rightarrow \frac{3}{5}\times \frac{12}{13}-\frac{4}{5}\times \frac{5}{13}=k\Rightarrow k=\frac{16}{65}$