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The function f x = 1 - sin x + cos x 1 + sin x + cos x is not defined at x = π . The value of f ( π ) , so that f ( x ) is continuous at x = π , is

Options

  1. A− 1 2
  2. B1 2
  3. C− 1
  4. D1

Correct answer

C. − 1

Step-by-step solution

l i m x → π   ( 1 + cos x ) - sin x ( 1 + cos x ) + sin x   = lim x → π 2 cos 2 x 2 − 2 sin x 2 cos x 2 2 cos 2 x 2 + 2 sin x 2 cos x 2 = lim x → π   1 − tan   x 2 1 + tan x 2 = l i m x → π tan ⁡ π 4 - x 2 = - 1 Since, f ( x ) is continuous at x = π ∴     f π = l i m x → π   f x = - 1

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