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Maths-

General

Easy

Question

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

1
$\frac{1}{2}$
2
$\frac{1}{4}$

hint Hint:

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

The correct answer is: 2

$L t subscript x rightwards arrow 0 end subscript fraction numerator left parenthesis 1 minus cos space 2 x right parenthesis left parenthesis 3 plus cos space x right parenthesis over denominator x tan space 4 x end fraction equals L t subscript x rightwards arrow 0 end subscript space fraction numerator open parentheses 1 minus 1 plus 2 sin squared x close parentheses open parentheses 3 plus cos x close parentheses over denominator x.4 x end fraction fraction numerator 4 x over denominator tan 4 x end fraction space space space space space space space space space space space space space space space space space space space open square brackets cos space 2 x equals 1 minus 2 sin squared x close square brackets equals L t subscript x rightwards arrow 0 end subscript fraction numerator 2 sin squared x over denominator 4 x squared end fraction space L t subscript x rightwards arrow 0 end subscript open parentheses 3 plus cos x close parentheses L t subscript x rightwards arrow 0 end subscript fraction numerator 4 x over denominator tan 4 x end fraction equals 1 half L t subscript x rightwards arrow 0 end subscript fraction numerator sin squared x over denominator x squared end fraction space L t subscript x rightwards arrow 0 end subscript open parentheses 3 plus cos x close parentheses L t subscript x rightwards arrow 0 end subscript fraction numerator 4 x over denominator tan 4 x end fraction equals 1 half open parentheses 3 plus 1 close parentheses 1 equals 4 over 2 equals 2$

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