Question

If tan $\theta =\frac{8}{15},$ then the value of $\frac{17sin\theta +\frac{5}{cos\theta }}{5tan\theta +\frac{8}{sin\theta }}$is

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

Answer 1

The correct option is C $\frac{41}{59}$

$tan\theta =\frac{8}{15}=\frac{perpendicular}{base}$
Therefore
$perpendicular=8$
$base=15$
$hypotenuse=\sqrt{perpendicula{r}^2+bas{e}^2}=\sqrt{8^2+{15}^2}$
$hypotenuse=17$ ...(i)
Hence $sin\theta =\frac{8}{17}$ and $cos\theta =\frac{15}{17}$ ...(ii)
Substituting in the expression we get
$\frac{17sin\theta +\frac{5}{cos\theta }}{5tan\theta +\frac{8}{sin\theta }}$
$=\frac{8+\frac{17}{3}}{\frac{8}{3}+17}$
$=\frac{41}{59}$
Hence answer is C