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📐 Mathematics  ·  Trigonometric Functions  ·  JEE

If sinθ + cosθ = 1/2, then sin2θ equals:

Answer: −3/4.

  • A 3/4
  • B −3/4
  • C 1/4
  • D −1/4

Correct answer: B. −3/4

Explanation: Squaring: 1 + sin2θ = 1/4, so sin2θ = −3/4.

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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