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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

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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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