Maths-
General
Easy

Question

Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator tan begin display style space end style x minus sin space x over denominator x squared end fraction equals

  1. 1
  2. 1 half
  3. -1
  4. 0

Hint:

In the question we will simplify the equation using some trigonometric identities, then at last we will put the value of x.

The correct answer is: 0


    Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator tan begin display style space end style x minus sin space x over denominator x squared end fraction
equals limit as x rightwards arrow 0 of fraction numerator begin display style fraction numerator sin x over denominator cos x end fraction end style minus sin x over denominator x squared end fraction
equals limit as x rightwards arrow 0 of fraction numerator begin display style fraction numerator sin x minus sin x space cos x over denominator cos x end fraction end style over denominator x squared end fraction
equals limit as x rightwards arrow 0 of fraction numerator sin x left parenthesis 1 minus cos x right parenthesis over denominator x squared. cos x end fraction
equals limit as x rightwards arrow 0 of fraction numerator sin x space over denominator x end fraction fraction numerator x over denominator cos x end fraction fraction numerator 1 minus cos x over denominator x squared end fraction
equals limit as x rightwards arrow 0 of fraction numerator sin space x over denominator x end fraction limit as x rightwards arrow 0 of fraction numerator x over denominator cos space x end fraction limit as x rightwards arrow 0 of fraction numerator 2 sin squared begin display style x over 2 end style over denominator open parentheses begin display style x over 2 end style close parentheses squared 4 end fraction space space space space space space space space space space space space space space space space space space open square brackets cos space 2 x equals 1 minus 2 sin squared x close square brackets
equals 1. fraction numerator 0 over denominator cos 0 end fraction.2
equals 0

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