Question

If in a $\Delta ABC;\frac{\cos A}{7}=\frac{\cos B}{19}=\frac{\cos C}{25}=k$, then $\left|\begin{array}{ccc}-1/k& 25& 19\\ 25& -1/k& 7\\ 19& 7& -1/k\end{array}\right|=$

• A. $-1$
• B. $1$
• C. $2$
• D. $0$

Answer 1

The correct option is D $0$

$△=\left|\begin{array}{ccc}\frac{-1}{K}& 25& 19\\ 25& \frac{-1}{K}& 7\\ 19& 7& \frac{-1}{K}\end{array}\right|$

$△=(\frac{1}{K^2}-49)+25(\frac{25}{K}-133)+19(175+\frac{19}{K})$

$△=\frac{1}{K^2}-49+\frac{986}{K}$

$\frac{\cos A}{7}=\frac{\cos B}{19}=\frac{\cos C}{25}=K$

$\Rightarrow △=0$