Question

In a $\Delta ABC$ , $\cos A=\frac{3}{5}$ and $\cos B=\frac{5}{13}$. The value of cos C can be

• A. $\frac{7}{13}$
• B. $\frac{47}{65}$
• C. $\frac{17}{65}$
• D. None of these

Answer 1

Answer: (C)

$\frac{17}{65}$

$cosA=\frac{3}{5}$ $cosB=\frac{5}{13}$

$A+B+C=\pi$
$A+B=\pi -C$

$cos(A+B)=cos(\pi -c)$
$cosAcosB-sinAsinB=-cosC$

$\left(\frac{3}{5}\right)\left(\frac{5}{13}\right)-\left(\frac{4}{5}\right)\left(\frac{8}{13}\right)=-cosC$

$cosC=\frac{32-15}{65}=\frac{17}{65}$