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BITSAT2019MathematicsLimitsActual

The value of lim x → 3 π 4 4 sin 2 x cos x - cos x + sin x sin x + cos x is

Options

  1. A- 1
  2. B0
  3. C1
  4. DNone of these

Correct answer

A. - 1

Step-by-step solution

L = lim x → 3 π 4 4 sin 2 x cos x - cos x + sin x sin x + cos x L = lim x → 3 π 4 2 sin x sin 2 x + cos 2 x + 2 sin x cos x - 1 - cos x + sin x sin x + cos x L = lim x → 3 π 4 2 sin x ( sin x + cos x ) 2 - 1 - cos x + sin x sin x + cos x L = lim x → 3 π 4 2 sin x ( sin x + cos x ) 2 - 2 sin x - cos x + sin x sin x + cos x L = lim x → 3 π 4 sin x + cos x 2 sin x sin x + cos x - 1 sin x + cos x L = lim x → 3 π 4 2 sin x sin x + cos x - 1 = - 1

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