Question

If $7\sin \alpha =24\cos \alpha ;0<\alpha <\frac{\pi }{2},$ then value of $14\tan \alpha -75\cos \alpha -7\sec \alpha$ is equal to

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (B)

$2$

Given,

$7\sin \alpha =24\cos \alpha$
$\Rightarrow \tan \alpha =\frac{24}{7}$
Now,

$\sec \alpha =\sqrt{1+{\tan }^2\alpha }$

$=\sqrt{1+\frac{576}{49}}$

$=\sqrt{\frac{625}{49}}$

$=\frac{25}{7}$

$\therefore \cos \alpha =\frac{7}{25}$
$\therefore 14\tan \alpha -75\cos \alpha -7\sec \alpha =14\left(\frac{24}{7}\right)-75\left(\frac{7}{25}\right)-7\left(\frac{25}{7}\right)$
$=48-21-25$
$=2$