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📐 Mathematics  ·  Trigonometric Functions  ·  JEE

cos 2A = 1 - 2sin²A. Verify for A = 30°:

Answer: cos 60° = 1/2 and 1-2sin²30° = 1/2 (true).

  • A cos 60° = 1/2 and 1-2sin²30° = 1/2 (true)
  • B cos 60° = √3/2, mistakenly using the cos 30° value instead
  • C They are not equal, since sin²30° was computed as 3/4 in error
  • D The identity only works for A = 0, where both sides trivially vanish

Correct answer: A. cos 60° = 1/2 and 1-2sin²30° = 1/2 (true)

Explanation: cos 60° = 1/2. 1 - 2sin²30° = 1 - 2(1/4) = 1/2. Equal. Identity verified.

xy0 deg30 deg45 deg (1/sqrt2, 1/sqrt2)60 deg90 degcos45sin45

Unit circle with standard angles 0, 30, 45, 60, 90 degrees; at 45 degrees the point is (cos45, sin45) = (1/sqrt2, 1/sqrt2).

Concept context

Ratios, identities, and applications in triangles

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