. lim 22 -(cosx + sin x 1-sin 2x 12...
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. lim 22 -(cosx + sin x 1-sin 2x 12 sina

JEE/Engineering Exams
Maths
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1.) ( lim _{x rightarrow pi / 4} frac{2 sqrt{2}-(cos x+sin x)^{3}}{1-sin 2 x} ) ( frac{0}{0} ) form a plely l'Hopital's rule ( =lim _{x rightarrow pi / 4} frac{left.|ln x| 2 sqrt{2}-(cos x+sin x)^{3}right]}{d x cdot[1-sin 2 x]} ) ( =lim _{x rightarrow pi / 4} frac{-3(cos x+sin x)^{2} cdot(-sin x+cos x)}{operatorname{tg} cos 2 x} ) Again ( frac{0}{0} ) form is Apply L'H sule: ( =lim _{x rightarrow pi / 4}left[frac{6(cos x+sin x)(cos x-sin x)^{2}+3(cos x+sin x)^{2}left(-cos x-sin ^{2} xright)}{-4 sin 2 x}right. ) ( frac{left(Y_{J 2}+Y_{sqrt{2}}right)left(Y_{Gamma_{2}}-Y_{Gamma 2}right)^{2}+3left(1 / sqrt{2}+Y_{Omega}right)^{2}left(-1 / 8_{2}-Psi_{Gamma_{2}}right)}{-4 sin pi_{2}} ) ( 0+3(2 / sqrt{2})^{2}(-2 sqrt{3}) ) -4 ( =3 times 2 times-7 / sqrt{2} ) ( -x ) ( =-frac{3}{sqrt{2}} )
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