If tan θ + 1/tan θ = 2, find the value of tan^2 θ + 1/tan^2 θ

Q) If tan θ + 1 / tan θ = 2, find the value of tan^2 θ + 1/ tan^2 θ.

(Q 24 A – 30/2/1 – CBSE 2026 Question Paper)

Ans:

Step 1: Given that, $\tan \theta + \frac{1}{\tan \theta} = 2$

By squaring on both sides we get:

$(\tan \theta + \frac{1}{\tan \theta})^2 = (2)^2$

∴ $(\tan \theta + \frac{1}{\tan \theta})^2 = 4$

Step 2: ∵ (a + b) ² = a ² + b ² + 2 a b

∴ Our expression becomes:

$(\tan \theta + \frac{1}{\tan \theta})^2 = 4$

∴ $(\tan \theta)^2 + (\frac{1}{\tan \theta})^2 + 2 (\tan \theta) \times (\frac{1}{\tan \theta}) = 4$

∴ $(\tan \theta)^2 + (\frac{1}{\tan \theta})^2 + 2 \cancel{(\tan \theta)} \times (\frac{1}{\cancel{\tan \theta}}) = 4$

∴ $\tan^2 \theta + \frac{1}{\tan^2 \theta} + 2 = 4$

∴ $\tan^2 \theta + \frac{1}{\tan^2 \theta} = 4 - 2 = 2$

Therefore, the value of $\tan^2 \theta + \frac{1}{\tan^2 \theta}$ is 2.

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