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If \(\tan 6\theta \cdot \tan 3\theta = 1\), where \(0 < \theta < 30^\circ\), then what is \(\theta\) equal to?

This question was previously asked in
CDS 2 2026 Maths Question Paper (13-Sep-2026)
The correct answer is

10°

\(\tan 6\theta \cdot \tan 3\theta = 1\) means \(\tan 6\theta = \cot 3\theta = \tan(90^\circ-3\theta)\). So \(6\theta = 90^\circ-3\theta\), giving \(9\theta = 90^\circ\), i.e. \(\theta = 10^\circ\), which lies in \(0<\theta<30^\circ\). The correct option is (b).

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