1) f(x)=cos3xsin3x
2) f(x)=cos^2 2x-sin^2 2x
3) f(x)=4\1+tg^2x
4) f(x)=cos^4 3x-sin^4 3x
f(x)=(1/2) sin6x
-1 ≤ sin6x ≤ 1
-1/2 ≤ (1/2)sin6x ≤ 1/2
О т в е т. [-1/2; 1/2]
2) f(x)=cos^22x–sin^22x
f(x)=cos4x
-1 ≤ cos 4x ≤ 1
О т в е т. [-1; 1]
3) f(x)=4/(1+tg^2x)
Формула 1+tg^2x=1/cos^2x ⇒ cos^2x= 1/(1+tg^2x)
f(x)=4cos^2x=4*(1+cos2x)/2=2+2cos2x
-1 ≤ cos2x ≤ 1
-2 ≤ 2cos2x ≤ 2
-2+2 ≤2+ 2cos2x ≤2+ 2
0 ≤2+ 2cos2x ≤4
О т в е т. [0;4]
4) f(x)=cos^4 3x–sin^4 3x
cos^4 3x–sin^4 3x=(cos^23x-sin^23x)*(cos^23x+sin^23x)=cos6x
-1 ≤ cos6x ≤ 1
О т в е т. [-1; 1]