Given A = sin20 + cos40, then for all real e, (A) 1 SAS 2 VI V VI VI is

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( begin{aligned} A &=sin ^{2} theta+cos ^{4} theta=sin ^{2} theta+left(1-sin ^{2} thetaright)^{2} &=sin ^{2} theta+1+sin ^{4} theta-2 sin ^{2} theta &=1+sin ^{4} theta-sin ^{2} theta &=1+sin ^{2} thetaleft(sin ^{2} theta-1right) &=frac{1-frac{4}{4} sin ^{2} theta cos ^{2} theta}{-1}=1-frac{sin ^{2} 2 theta}{4} &=frac{1}{4} leqslant frac{sin ^{2} 2 theta}{4} leqslant frac{1}{4} & frac{-1}{4} leqslant frac{-sin ^{2} 2 theta}{4} leq 0 frac{3}{4} leq & frac{1-sin ^{2} 2 theta}{4} leqslant 1 & frac{3}{4} leqslant A leqslant 1 end{aligned} )

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