Question

IF $\tan \Theta =\frac{8}{15}$ then the value of $\frac{17\sin \Theta +\frac{5}{\cos \Theta }}{5\tan \Theta +\frac{8}{\sin \Theta }}$

• A. $\frac{59}{41}$
• B. $\frac{35}{41}$
• C. $\frac{41}{59}$
• D. $\frac{41}{35}$

Answer 1

Answer: (C)

$\frac{41}{59}$

We have,

$\tan \theta =\frac{8}{15}$

So, $Height=8,Base=15$

Then, $Hypotenuse=17$

$\sin \theta =\frac{8}{17}$

$\cos \theta =\frac{15}{17}$

Since,

$=\frac{17\sin \theta +\frac{5}{\cos \theta }}{5\tan \theta +\frac{8}{\sin \theta }}$

$=\frac{8+\frac{17}{3}}{\frac{8}{3}+17}$

$=\frac{\frac{24+17}{3}}{\frac{8+51}{3}}$

$=\frac{41}{59}$

Hence, this is the answer.