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Question 200030
JEE Mathematics · Hard

Trigonometry: Inequality MCQ

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

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InequalityHardQuestion 200030

Question

The number of values of x in [0, 2π] satisfying sin x > cos x is:
  1. A
    x in (π/4, 5π/4)
    Correct
  2. B
    x in (0, π/4)
  3. C
    x in (π/4, π)
  4. D
    x in (3π/4, 2π)

Correct answer

x in (π/4, 5π/4)

Explanation

sin x > cos x → sin x − cos x > 0 → √2 sin(x − π/4) > 0 → sin(x − π/4) > 0. This holds when x − π/4 ∈ (0, π) i.e. x ∈ (π/4, 5π/4).

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