Question

If $tanA=\frac{3}{4}$, find the value of $\frac{2sinAcosA}{co{s}^{2}A-si{n}^{2}A}$

Answer 1

Given that $tanA=\frac{3}{4}$

$\frac{2sinAcosA}{co{s}^{2}A-si{n}^{2}A}=\frac{sin2A}{cos2A}$

$=tan2A$

$=\frac{2tanA}{1-ta{n}^{2}A}$

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

$=\frac{\frac{3}{2}}{\frac{7}{16}}=\frac{24}{7}$