Ex 3.3, 24 - Prove cos 4x = 1 - 8 sin2 x cos 2 x - Chapter 3 - Ex 3.3

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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Ex 3.3, 24 Prove that cos 4๐‘ฅ = 1 โ€“ 8sin2 ๐‘ฅ cos2 ๐‘ฅ Taking L.H.S. cos 4x = 2(cos 2x)2 โ€“ 1 = 2 ( 2 cos2 x โ€“ 1)2 -1 Using (a โ€“ b)2 = a2 + b2 โ€“ 2ab = 2 [(2cos x)2 + (1)2 โ€“ 2 ( 2cos2x ) ร— 1] โ€“ 1 = 2 (4cos4x + 1 โ€“ 4 cos2x ) โ€“ 1 = 2 ร— 4cos4x + 2 ร— 1โ€“ 2 ร— 4 cos2x โ€“ 1 = 8cos4x + 2 โ€“ 8 cos2x -1 = 8cos4x โ€“ 8 cos2x + 2 โ€“ 1 = 8cos4x โ€“ 8 cos2x + 1 = 8cos2x (cos2x โ€“ 1) + 1 = 8cos2x [โ€“ (1 โ€“ cos2x)] + 1 = โ€“8cos2x [(1 โ€“ cos2x )] + 1 = โ€“ 8cos2x sin2x + 1 = 1 โ€“ 8 cos2x sin2x = R.H.S. Hence R.H.S. = L.H.S. Hence proved

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