Pertanyaan

N i l ai d a r i x → 4 π lim cos x − sin x cos 2 x = ....

$N i l ai d a r i x \to \frac{π}{4} lim \frac{cos 2 x}{cos x - sin x} = ....$

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$limit as x rightwards arrow pi over 4 of fraction numerator cos 2 x over denominator cos x minus sin x end fraction equals limit as x rightwards arrow pi over 4 of fraction numerator negative 2 sin 2 x over denominator negative sin x minus cos x end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator negative 2 sin 2 x over denominator negative sin x minus cos x end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator negative 2 sin 2 open parentheses begin display style pi over 4 end style close parentheses over denominator negative sin open parentheses pi over 4 close parentheses minus cos open parentheses pi over 4 close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator negative 2 left parenthesis 1 right parenthesis over denominator negative begin display style 1 half end style square root of 2 minus begin display style 1 half end style square root of 2 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator negative 2 over denominator negative square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals square root of 2$