Question

If $\cos A=\frac{3}{5}$, evaluate $\frac{5\sin A+3\sec A-3\tan A}{4\cot A+4cosecA+5\cos A}$.

• A. $\frac{5}{11}$
• B. $\frac{7}{11}$
• C. $\frac{9}{11}$
• D. $\frac{1}{11}$

Answer 1

The correct option is A $\frac{5}{11}$

$cosA=\frac{3}{5}$
$secA=\frac{5}{3}$
Hence
$sinA=\frac{4}{5}$
$tanA=\frac{4}{3}$
Hence substituting in the above expression, we get
$\frac{4+5-4}{3+5+3}$
$=\frac{5}{11}$