Question

If $7\sin A=24\cos A$, then $14\tan A+25\cos A-7\sec A$ equals

• A. $0$
• B. $1$
• C. $30$
• D. $32$

Answer 1

Answer: (C)

$30$

Given, $7\sin A=24\cos A$

$\Rightarrow \frac{\sin A}{\cos A}=\frac{24}{7}$

$\Rightarrow \tan A=\frac{24}{7}$
$\Rightarrow \tan A=\frac{P}{B}$
Using Pythagoras theorem, we have

$H^2=P^2+B^2$
$H^2={24}^2+7^2$
$H^2=625$
$H=25$
Now, $14\tan A+25\cos A-7\sec A$

$=$ $14\left(\frac{P}{B}\right)+25\left(\frac{B}{H}\right)-7\left(\frac{H}{B}\right)$

$=$ $14\left(\frac{24}{7}\right)+25\left(\frac{7}{25}\right)-7\left(\frac{25}{7}\right)$
$=$ $48+7-25$
$=$ $30$