হলে,  ফাংশনের সর্বোচ্চ মান কত হবে?

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NDA 01/2022: Maths Previous Year paper (Held On 10 April 2022)
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NDA 01/2025: English Subject Test
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অনুসৃতসূত্র:

  • sin θ/cos θ = tan θ
  • cos θ/sin θ = cot θ
  • sin2θ + cos2θ = 1
  • 2sin θ cos θ = sin 2θ

 

গণনা:

⇒ f(x) = sin x cos x ( ) [∵ sin2θ + cos2θ = 1]

⇒ f(x) = sin 2x       [∵ 2sin θ cosθ = sin 2θ]

আমরা জানি যে, -1 ≤ sin θ ≤ 1

-1 ≤ sin 2x ≤ 1

∴ f(x)সর্বোচ্চ = (1) = 1/2

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