NVAMediumJEE Main 2023 · 25 January, Shift 2Trigonometric Equations

Mathematics Question from JEE Main 2023 · 25 January, Shift 2

If mm and nn respectively are the numbers of positive and negative values of θ\theta in the interval [π,π][-\pi, \pi] that satisfy the equation cos2θcosθ2=cos3θcos9θ2\cos 2\theta \cdot \cos\frac{\theta}{2} = \cos 3\theta \cdot \cos\frac{9\theta}{2}, then mnmn is equal to:

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