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# If $\Tan \Theta = \Frac{3}{4}$, Find the Values of Sec​θ and Cos​θ - Geometry

ConceptApplication of Trigonometry

#### Question

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

#### Solution

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.

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#### APPEARS IN

Balbharati Solution for Balbharati Class 10 Mathematics 2 Geometry (2018 to Current)
Chapter 6: Trigonometry
Practice set 6.1 | Q: 2 | Page no. 131
Solution If $\Tan \Theta = \Frac{3}{4}$, Find the Values of Sec​θ and Cos​θ Concept: Application of Trigonometry.
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