Chapter 7: Q. 9 (page 506)

Find the exact value of $\cos (\tan^{- 1} 2)$ .

Short Answer

Expert verified

The required value is $\frac{\sqrt{5}}{5}$ .

Step by step solution

Step 1. Given Information

We need to find the value of the trigonometric function $\cos (\tan^{- 1} 2)$ .

Step 2. Finding the value

Let $θ = \tan^{- 1} 2 \Rightarrow \tan θ = 2$

The interval of tangent function is $0 < θ < \frac{π}{2}$ since $\tan θ > 0$ .

The hypotenuse is $\sqrt{2^{2} + 1^{2}} = \sqrt{5}$ .

$∴ \cos θ = \frac{1}{\sqrt{5}} \Rightarrow \cos θ = \frac{\sqrt{5}}{\sqrt{5} \times \sqrt{5}} \Rightarrow \cos θ = \frac{\sqrt{5}}{5}$

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Find the exact value of $\cos (\tan^{- 1} 2)$ .

Short Answer

Step by step solution

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Step 2. Finding the value

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