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Problem If y = sin x sin 3 x y = \sin x \sin 3x y = sin x sin 3 x y n = y_n = y n = 1 2 [ cos ( 2 x + n π 2 ) − cos ( 4 x + n π 2 ) ] \frac{1}{2} \left[ \cos \left( 2x + n \frac{\pi}{2} \right) - \cos \left( 4x + n \frac{\pi}{2} \right) \right] 2 1 [ cos ( 2 x + n 2 π ) − cos ( 4 x + n 2 π ) ] 1 2 [ 2 n cos ( 2 x + n π 2 ) − 4 n cos ( 4 x + n π 2 ) ] \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] 2 1 [ 2 n cos ( 2 x + n 2 π ) − 4 n cos ( 4 x + n 2 π ) ] 1 2 [ 4 n cos ( 4 x + n π 2 ) − 2 n cos ( 2 x + n π 2 ) ] \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] 2 1 [ 4 n cos ( 4 x + n 2 π ) − 2 n cos ( 2 x + n 2 π ) ] Browse the problem library