If \(\tan\theta + \cot\theta = 2\), where \(0^\circ < \theta < 90^\circ\), find \(\tan^{10}\theta + \cot^{10}\theta\).

A. 2

B. 10

C. 1

D. \(2^{10}\)

Doubtly AI Asked 27 Oct 2026 AI-generated · not yet verified ssc cpo Save WhatsApp Report

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Answer: A. 2

Answer: (A) 2

Let \(t = \tan\theta\). \(t + \frac{1}{t} = 2\) gives \((t - 1)^2 = 0\), so \(t = 1\) (θ = 45°).

Then \(\tan^{10}\theta + \cot^{10}\theta = 1 + 1 = 2\).

Doubtly AI · 27 Oct 2026 AI-generated · not yet verified Report

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