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# Prave That: If Tan θ + 1 Tan θ = 2 , Then Show that Tan 2 θ + 1 Tan 2 θ = 2 - Geometry

ConceptApplication of Trigonometry

#### Question

Prove that:
If $\tan\theta + \frac{1}{\tan\theta} = 2$, then show that $\tan^2 \theta + \frac{1}{\tan^2 \theta} = 2$

#### Solution

$\tan\theta + \frac{1}{\tan\theta} = 2$
Squaring on both sides, we get
$\left( \tan\theta + \frac{1}{\tan\theta} \right)^2 = 2^2$
$\Rightarrow \tan^2 \theta + \frac{1}{\tan^2 \theta} + 2 \times \tan\theta \times \frac{1}{\tan\theta} = 4$ ... (using (a + b)2 = a2 + 2ab + b2)
$\Rightarrow \tan^2 \theta + \frac{1}{\tan^2 \theta} + 2 = 4$
$\Rightarrow \tan^2 \theta + \frac{1}{\tan^2 \theta} = 4 - 2 = 2$

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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: 6.09 | Page no. 131
Solution Prave That: If Tan θ + 1 Tan θ = 2 , Then Show that Tan 2 θ + 1 Tan 2 θ = 2 Concept: Application of Trigonometry.
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