Ex 3.3, 10 - Prove that sin (n + 1)x sin (n + 2)x + cos (n+1)x - Ex 3.3

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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E𝑥3.3, 10 Prove that sin⁡(𝑛 + 1)𝑥 sin⁡(𝑛 + 2)𝑥+cos⁡(𝑛 + 1)𝑥 cos⁡(𝑛 + 2)𝑥=cos⁡𝑥 Taking L.H.S. We know that cos ( A – B) = cos A cos B + sin A sin B Hence A = (n + 1)x ,B = (n + 2)x Hence sin⁡(𝑛 + 1)𝑥 sin⁡(𝑛 + 2)𝑥+cos⁡(𝑛 + 1)𝑥 cos⁡(𝑛 + 2)𝑥 = cos [ (n + 1)x – (n + 2)x ] = cos [ nx + x – nx – 2x ] = cos [ nx – nx – x – 2 x ] = cos (0 – x )   = cos (– x) = cos x = R.H.S. Hence , L.H.S. = R.H.S. Hence proved

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