[Solved] If Cos 4x = 1 + K Sin2 X Cos2 X, Then Find The Value Of K ?

Trang chủ » Sin Bình X + Cos Bình 4x = 1 » [Solved] If Cos 4x = 1 + K Sin2 X Cos2 X, Then Find The Value Of K ?

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Concept:

  • cos 2x = cos2 x – sin2 x
  • sin 2x = 2 sin x cos x

Calculation:

Given: cos 4x = 1 + k sin2 x cos2 x

As we know that, cos 2x = cos2 x – sin2 x

⇒ cos 4x = cos (2 × 2x) = cos2 (2x) – sin2 (2x) = 1 – 2 sin2 (2x)

⇒ cos 4x = 1 - 2 sin2 (2x) = 1 – 2 (2 sin x cos x)2

⇒ cos 4x = 1 – 8 sin2 x cos2 x

∵ cos 4x = 1 + k sin2 x cos2 x -----(Given)

⇒ 1 – 8 sin2 x cos2 x = 1 + k sin2 x cos2 x

⇒ k = -8

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Từ khóa » Sin Bình X + Cos Bình 4x = 1