Решите №2 под цифрами 5, 6, 7.

$2Cos^4a+Sin^22a+2Sin^4a=2$

$2Cos^4a+(2Sina*Cosa)^2+2Sin^4a=$

$=2Cos^4a+4Sin^2a*Cos^2a+2Sin^4a=$

$=( \sqrt{2}Cos^2a)^2+2 \sqrt{2} \sqrt{2}Sin^2aCos^2a+( \sqrt{2}Sin^2a)^2=$

$=( \sqrt{2}Cos^2a+ \sqrt{2}Sin^2a)^2= \sqrt{2}^2=2$

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$1+Sina=2Cos^2( \frac{ \pi }{4}- \frac{a}{2})$

$2(Cos( \pi /4-a/2))^2=2(Cos(\pi /4)*Cos(a/2)+Sin(\pi /4)*Sin(a/2))^2=$

$=2( \sqrt{2}/2*Cos(a/2)+ \sqrt{2}/2*Sin(a/2))^2=(Cos(a/2)+Sin(a/2))^2=$

$=Cos^2(a/2)+2*Cos(a/2)Sin(a/2)+Sin^2(a/2)=1+sina$

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$1-Sina=2Cos^2( \frac{ \pi }{4}+ \frac{a}{2})$

$2(Cos( \pi /4+a/2))^2=2(Cos(\pi /4)*Cos(a/2)-Sin(\pi /4)*Sin(a/2))^2=$

$=2( \sqrt{2}/2*Cos(a/2)- \sqrt{2}/2*Sin(a/2))^2=(cos(a/2)-Sin(a/2))^2=$

$=Cos^2(a/2)-2Sin(a/2)Cos(a/2)+Sin^2(a/2)=1-Sina$