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Question

L t subscript x plus 0 end subscript fraction numerator left parenthesis 1 minus cos space 2 x right parenthesis left parenthesis 3 plus cos space x right parenthesis over denominator x tan space 4 x end fraction text  is equal to  end text

  1. 1
  2. 1 half
  3. 2
  4. 1 fourth

hintHint:

In this question, we have to find value of L t subscript x rightwards arrow 0 end subscript fraction numerator left parenthesis 1 minus cos space 2 x right parenthesis left parenthesis 3 plus cos space x right parenthesis over denominator x tan space 4 x end fraction.

The correct answer is: 2


    L t subscript x rightwards arrow 0 end subscript fraction numerator left parenthesis 1 minus cos space 2 x right parenthesis left parenthesis 3 plus cos space x right parenthesis over denominator x tan space 4 x end fraction
    L t subscript x rightwards arrow 0 end subscript fraction numerator left parenthesis 1 minus cos space 2 x right parenthesis left parenthesis 3 plus cos space x right parenthesis over denominator x tan space 4 x end fraction = L t subscript x rightwards arrow 0 end subscript fraction numerator left parenthesis 2 sin squared x right parenthesis left parenthesis 3 plus cos space x right parenthesis over denominator x tan space 4 x end fraction space space space space W e space k o n w space t h a t space space left parenthesis 1 minus cos space 2 x right parenthesis space equals space 2 sin squared x space space
    L t subscript x rightwards arrow 0 end subscript fraction numerator 4 x over denominator tan space 4 x end fraction cross times fraction numerator left parenthesis sin squared x right parenthesis left parenthesis 3 plus cos space x right parenthesis over denominator 2 x squared end fraction space space space left parenthesis A l s o space W e space k n o w space t h a t space L t subscript x rightwards arrow 0 end subscript fraction numerator tan space x over denominator x end fraction equals 1 comma space L t subscript x rightwards arrow 0 end subscript fraction numerator sin x over denominator x end fraction equals space 1 right parenthesis
L t subscript x rightwards arrow 0 end subscript fraction numerator left parenthesis 3 plus cos space x right parenthesis over denominator 2 end fraction space
p u t space x equals 0 comma space t h e n
fraction numerator left parenthesis 3 plus cos space 0 right parenthesis over denominator 2 end fraction equals space 4 over 2 space equals 2

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