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Maths-

General

Easy

Question

$L subscript x not stretchy rightwards arrow 0 end subscript equals fraction numerator sin begin display style space end style open parentheses pi cos squared space x close parentheses over denominator x squared end fraction$ Is equal to

$π$
$- π$
$\frac{π}{2}$
1

hint Hint:

In the question we will simplify the equation using trigonometric identities.

The correct answer is: $pi$

$L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator sin begin display style space end style open parentheses pi cos squared space x close parentheses over denominator x squared end fraction equals L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator sin space open parentheses straight pi open parentheses 1 minus sin squared straight x close parentheses close parentheses over denominator x squared end fraction equals straight pi open curly brackets straight L subscript straight x not stretchy rightwards arrow 0 end subscript fraction numerator sin open parentheses straight pi minus πsin squared straight x close parentheses over denominator πsin squared straight x end fraction cross times fraction numerator sin squared straight x over denominator straight x squared end fraction close curly brackets space space space space space space space space space open square brackets sin left parenthesis straight pi minus straight a right parenthesis equals sina close square brackets equals straight pi open curly brackets straight L subscript straight x not stretchy rightwards arrow 0 end subscript fraction numerator sin open parentheses πsin squared straight x close parentheses over denominator πsin squared straight x end fraction cross times fraction numerator sin squared straight x over denominator straight x squared end fraction close curly brackets space space space space space space space space space space space space equals straight pi cross times 1 cross times 1 equals straight pi$

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