Question

Решите №2 под цифрами 5, 6, 7.

Answer 1

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

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

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

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

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

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

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

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

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