Maharashtra State Board course SSC (English Medium) Class 10th Board Exam
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If \[\Tan \Theta = \Frac{3}{4}\], Find the Values of Sec​θ and Cos​θ - Geometry

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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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 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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