Ex 13.1, 21 - Evaluate: lim x->0 (cosec x - cot x) - Class 11 - Limits - Of Trignometric functions

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  1. Chapter 13 Class 11 Limits and Derivatives
  2. Serial order wise
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Ex 13.1, 21 (Method 1) Evaluate the Given limit: lim (x 0) (cosec x cot x) lim (x 0) (cosec x cot x) = lim (x 0) (1/sin cos /sin ) = lim (x 0) (1 cos )/sin Putting x = 0 = (1 cos 0 )/sin 0 = (1 1)/0 = 0/0 Hence, we need to simplify lim (x 0) (1 cos )/sin = lim (x 0) (1 cos )/sin ( + )/( + ) = lim (x 0) (1^2 cos^2 )/(sin (1 + cos ) ) = lim (x 0) ( ^ )/(sin (1 + cos ) ) = lim (x 0) ^ /(sin (1 + cos ) ) = lim (x 0) /((1 + cos ) ) Putting x = 0 = 0/((1 + cos 0 ) ) = 0/(1 + 1) = 0/2 = 0

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