A Level

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

If y=sin⁡xsin⁡3xy = \sin x \sin 3x , then yn=y_n = (a) 12[cos⁡(2x+nπ2)−cos⁡(4x+nπ2)]\frac{1}{2} \left[ \cos \left( 2x + n \frac{\pi}{2} \right) - \cos \left( 4x + n \frac{\pi}{2} \right) \right] (b) 12[2ncos⁡(2x+nπ2)−4ncos⁡(4x+nπ2)]\frac{1}{2} \left[ 2^n \cos \left( 2x + n \frac{\pi}{2} \right) - 4^n \cos \left( 4x + n \frac{\pi}{2} \right) \right] (c) 12[4ncos⁡(4x+nπ2)−2ncos⁡(2x+nπ2)]\frac{1}{2} \left[ 4^n \cos \left( 4x + n \frac{\pi}{2} \right) - 2^n \cos \left( 2x + n \frac{\pi}{2} \right) \right] (d) None of these

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