B3

Дано

[tex]\displaystyle cos2a=0.6\\\\cos^22a+sin^22a=1; sin^22a=1-cos^22a=1-0.36=0.64[/tex]

упростим выражение

[tex]\displaystyle (cos^3a)^2-(sin^3a)^2=(cos^3a-sin^3a)*(cos^3a+sin^3a)=\\\\=(cosa-sina)(cos^2a+cosa*sina+sin^2a)*(cosa+sina)(cos^2a-cosa*sina+sin^2a)=\\\\=(cos^2a-sin^2a)(1+cosa*sina)(1-cosa*sina)=\\\\(cos2a)*(1-(cosa*sina)^2)=(cos2a)*(1-\frac{1}{4}(2cosa*sina)^2)=\\\\=cos2a*(1-\frac{1}{4}sin^22a)=0.6*(1-\frac{1}{4}*0.64)=0.6*0.84= 0.504[/tex]

B4

Дано:

[tex]\displaystyle ctga=3=\frac{cosa}{sina}; cosa=3sina[/tex]

Упростим выражение

[tex]\displaystyle\frac{cos2a+3(cos^2a+sin^2a)}{2sin2a-(cos^2a+sin^2a)}=\frac{cos^2a-sin^2a+3cos^2a+3sin^2a}{4sina*cosa-cos^2a-sin^2a}=\\\\=\frac{4cos^2a+2sin^2a}{4sina*cosa-cos^2a-sin^2a}[/tex]

заменим cosa=3sina

[tex]\displaystyle\frac{4(3sina)^2+2sin^2a}{4*sina*3sina-(3sina)^2-sin^2a}= \frac{36sin^2a+2sin^2a}{12sin^2a-9sin^2a-sin^2a}=\\\\=\frac{38sin^2a}{2sin^2a}=\frac{38}{2}=19[/tex]