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Question 200056
JEE Mathematics · Hard

Trigonometry: Maximum MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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MaximumHardQuestion 200056

Question

The maximum value of sin x(1 + cos x) is:
  1. A
    3√3/4
    Correct
  2. B
    3/4
  3. C
    √3/4
  4. D
    1

Correct answer

3√3/4

Explanation

f(x) = sin x + sin x cos x = sin x + (sin 2x)/2. Differentiating: cos x + cos 2x = 0 → cos x + 2cos²x − 1 = 0 → 2cos²x + cos x − 1 = 0 → cos x = 1/2 or −1. At cos x = 1/2 (x = π/3): f = (√3/2)(1 + 1/2) = 3√3/4.

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