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AP EAMCET202120 Aug 2021Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

What is the value of cos 22 1 2 ° =

Options

  1. A2 - 1 2 2
  2. B2 + 1 2 2
  3. C2 - 1
  4. D2 + 1

Correct answer

B. 2 + 1 2 2

Step-by-step solution

Let cos   A = cos 22 1 2 ∘ ⇒ A = 22 1 2 ∘ Using formula, cos   2 A = 2 cos 2 A - 1 ⇒ cos   45 ∘ = 2 cos 2 A - 1 ⇒ 1 2 + 1 = 2 cos 2 A ⇒ 2 cos 2 A = 1 + 2 2 ⇒ cos A = 1 + 2 2 2 Hence, cos   A = cos 22 1 2 ∘ = 1 + 2 2 2

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