Misc 7 - Prove sin 3x + sin2x - sin x = 4 sin x cos x/2 cos 3x/2 - cos x + cos y formula

  1. Class 11
  2. Important Question for exams Class 11
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Misc 7 Prove that: sin 3x + sin2x – sin x = 4 sin x cos π‘₯/2 cos 3π‘₯/2 Solving L.H.S sin 3x + sin 2x - sin x = sin 3x + (sin 2x – sin x ) = sin 3x + [2cos ((2π‘₯ + π‘₯)/2) . sin ((2π‘₯βˆ’π‘₯)/2)] = sin 3x + [ 2cos (3π‘₯/2) sin π‘₯/2] = 2sin 3π‘₯/2 cos 3π‘₯/2 + [ 2 cos 3π‘₯/2 sin π‘₯/2 ] = 2cos 3π‘₯/2 [ sin 3π‘₯/2 + sin π‘₯/2 ] = 2 cos 3π‘₯/2 [2 sin ("(" 3π‘₯/2 " + " π‘₯/2 ")" )/2 . cos ("(" 3π‘₯/2 " βˆ’ " π‘₯/2 ")" )/2] = 2 cos 3π‘₯/2 [ 2 sin ("(" (3π‘₯ + π‘₯)/2 ")" )/2 . cos ("(" (3π‘₯ βˆ’ π‘₯)/2 ")" )/2] = 2 cos 3π‘₯/2 [ 2 sin ("(" 4π‘₯/2 ")" )/2 . cos ("(" 2π‘₯/2 ")" )/2] = 2 cos 3π‘₯/2 [ 2 sin ("(" 2π‘₯/1 ")" )/2 . cos ("(" π‘₯/1 ")" )/2] = 2 cos 3π‘₯/2 [ 2 sin 2π‘₯/2 . cos π‘₯/2] = 2 cos 3π‘₯/2 [ 2 sin π‘₯ . cos π‘₯/2] = 4 cos 3π‘₯/2 sin π‘₯ cos π‘₯/2 = R.H.S Hence L.H.S = R.H.S Hence proved

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