Question
If $\tan \theta=\frac{3}{4}$ find the values of secθ and cosθ.
✓
Answer
We know that,
$\sec ^2 \theta=1+\tan ^2 \theta$
$\Rightarrow \sec ^2 \theta=1+\left(\frac{3}{4}\right)^2$
$\Rightarrow \sec ^2 \theta=1+\frac{9}{16}$
$\Rightarrow \sec ^2 \theta=\frac{25}{16}$
$\Rightarrow \sec \theta=\frac{5}{4}$
Also,
$\Rightarrow \cos \theta=\frac{1}{\sec \theta}$
$\Rightarrow \cos \theta=\frac{4}{5}$
$\sec ^2 \theta=1+\tan ^2 \theta$
$\Rightarrow \sec ^2 \theta=1+\left(\frac{3}{4}\right)^2$
$\Rightarrow \sec ^2 \theta=1+\frac{9}{16}$
$\Rightarrow \sec ^2 \theta=\frac{25}{16}$
$\Rightarrow \sec \theta=\frac{5}{4}$
Also,
$\Rightarrow \cos \theta=\frac{1}{\sec \theta}$
$\Rightarrow \cos \theta=\frac{4}{5}$
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