# If Tanθ = 2, Find the Values of Other Trigonometric Ratios. - Geometry

#### Question

If tanθ = 2, find the values of other trigonometric ratios.

#### Solution

tanθ = 2         (Given)

We have,

$\sec^2 \theta = 1 + \tan^2 \theta$
$\Rightarrow \sec\theta = \sqrt{1 + \tan^2 \theta}$
$\Rightarrow \sec\theta = \sqrt{1 + 2^2}$
$\Rightarrow \sec\theta = \sqrt{1 + 4} = \sqrt{5}$
$\therefore \cos\theta = \frac{1}{\sec\theta} = \frac{1}{\sqrt{5}}$
Now,
$\tan\theta = \frac{\sin\theta}{\cos\theta}$
$\Rightarrow \sin\theta = \tan\theta \times \cos\theta$
$\Rightarrow \sin\theta = 2 \times \frac{1}{\sqrt{5}} = \frac{2}{\sqrt{5}}$
$\therefore cosec\theta = \frac{1}{\sin\theta} = \frac{1}{\frac{2}{\sqrt{5}}} = \frac{\sqrt{5}}{2}$
Also,
$\cot\theta = \frac{1}{\tan\theta} = \frac{1}{2}$

Is there an error in this question or solution?