Question

$\mathrm{If}\cos \theta =\frac{2}{3},\mathrm{the}\mathrm{write}\mathrm{the}\mathrm{value}\mathrm{of}\left(4+4{\tan }^2\theta \right).$

Answer 1

$$\begin{gathered} 4+4{\tan }^2\theta \\ =4\left(1+{\tan }^2\theta \right) \\ =4{\sec }^2\theta \\ =\frac{4}{{\cos }^2\theta } \\ =\frac{4}{{\left({\displaystyle \frac{2}{3}}\right)}^2} \\ =\frac{4}{\left({\displaystyle \frac{4}{9}}\right)} \\ =\frac{4\times 9}{4} \\ =9 \end{gathered}$$