Trigonometry: Multiple Correct MCQ

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

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Multiple CorrectHardQuestion 200039

Question

Which of the following is/are CORRECT? (I) sin(x+y) can exceed 1 (II) |sin x + cos x| ≤ √2 (III) sin x · cos x ≤ 1/2

II and III only

(I) False: sin(x+y) ≤ 1 always. (II) |sin x + cos x| = √2 |sin(x+π/4)| ≤ √2. True. (III) sin x cos x = (sin 2x)/2 ≤ 1/2. True. So II and III.