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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?
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If Tanθ = 2, Find the Values of Other Trigonometric Ratios. Concept: Trigonometric Ratios of Complementary Angles.
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