Question

If \[\tan \theta = \frac{3}{4}\], find the values of sec​θ and cos​θ

Answer 1

We have,
\[\sec^2 \theta = 1 + \tan^2 \theta\]
\[ \Rightarrow \sec^2 \theta = 1 + \left( \frac{3}{4} \right)^2 \]
\[ \Rightarrow \sec^2 \theta = 1 + \frac{9}{16} = \frac{16 + 9}{16} = \frac{25}{16}\]
\[ \Rightarrow \sec\theta = \sqrt{\frac{25}{16}} = \frac{5}{4}\]
Now,

\[\cos\theta = \frac{1}{\sec\theta}\]

\[ \Rightarrow \cos\theta = \frac{1}{\left( \frac{5}{4} \right)}\]

\[ \Rightarrow \cos\theta = \frac{4}{5}\]
Thus, the values of sec​θ and cos​θ are \[\frac{5}{4}\] and \[\frac{4}{5}\], respectively.