Question

If $\theta$ is in the first quadrant and $\cos \theta =\frac{3}{5}$, then the value of $\frac{5\tan \theta -4cosec\theta }{5sec\theta -4\cot \theta }$ will be

• A. $\frac{5}{16}$
• B. $\frac{5}{34}$
• C. $-\frac{5}{34}$
• D. $-\frac{5}{16}$

Answer 1

The correct option is A $\frac{5}{16}$

$\because$ Since $\theta$ is in the first quadrant, all trigonometrical ratios will be positive.

and $\cos \theta =\frac{3}{5}$

then $\sin \theta =sqrt1-{\cos }^2\theta$

$=\sqrt{1-{\left(\frac{3}{5}\right)}^2}=\frac{4}{5}$

and $\tan \theta =\frac{4}{3}$

$\therefore$ Given, Exp. =$\frac{5\tan \theta -4cosec\theta }{5sec\theta -4\cot \theta }$

$=\frac{5\times \frac{4}{3}-4\times \frac{5}{4}}{5\times \frac{5}{3}-4\times \frac{3}{4}}$

$=\frac{5(\frac{4}{3}-1)}{\frac{25}{3}-3}$

$=\frac{\frac{5}{3}}{\frac{16}{3}}=\frac{5}{16}$