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1998

JEE Main 1998 Mathematics question on Trigonometry

Which of the following numbers is rational?
  1. A.
    sin⁡15°\sin 15°
  2. B.
    cos⁡15°\cos 15°
  3. C.
    sin⁡15°cos⁡15°\sin 15° \cos 15°
  4. D.
    sin⁡15°cos⁡75°\sin 15° \cos 75°
Show answer and solution

Correct option: C

Solution

sin15° cos15° = (1/2)sin30° = (1/2)(1/2) = 1/4, which is rational.

The key identity used is 2sinθcosθ = sin2θ, so sin15°cos15° = (sin30°)/2 = (1/2)/2 = 1/4.

[1998]

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