Question

If $5sin\theta =4$, then find the value of $\frac{sec\theta \times tan\theta }{sec\theta -tan\theta }$.

• A. $\frac{20}{3}$
• B. $\frac{3}{20}$
• C. $\frac{-20}{3}$
• D. $\frac{-3}{20}$

Answer 1

The correct option is A $\frac{20}{3}$


Given, $5sin\theta =4$
$\Rightarrow sin\theta =\frac{4}{5}\Rightarrow sec\theta =\frac{5}{3}\text{and}tan\theta =\frac{4}{3}\Rightarrow \frac{sec\theta \times tan\theta }{sec\theta -tan\theta }=\frac{\frac{5}{3}\times \frac{4}{3}}{\frac{5}{3}-\frac{4}{3}}=\frac{\frac{20}{9}}{\frac{1}{3}}=\frac{20}{3}$