`a)A=cos(2x)+3`

`=(2cos^2x-1)+3`

`=2cos^2x-1+3`

`=2cos^2x+2`

Ta có: `cosx\in[-1;1]->0<=cos^2x<=1`

`->2*0+2<=A=2cos^2x<=2*1+2`

`->2<=A<=4`

`->A_(max)=4` và `A_(min)=2`

`b)M=7cos^2x-2sin^2x`

`=7(1-sin^2x)-2sin^2x`

`=7-7sin^2x-2sin^2x`

`=7-9sin^2x`

Vì: `sinx\in[-1;1]->0<=sin^2x<=1`

`->7-9*1<=M=7-9sin^2x<=7-9*0`

`->-2<=M<=7`

Vậy: `M_(max)=7` khi `sinx=0` và `M_(min)=-2` khi `sin^2x=1`

`c)Q=sin^6x+cos^6x`

`=(sin^2x+cos^2x)^3-3sin^2x*cos^2x(sin^2x+cos^2x)`

`=1^3-3sin^2x*cos^2x*1`

`=1-3sin^2x*cos^2x`

`=1-3/4(2sinxcosx)^2`

`=1-3/4sin^2(2x)`

Vì: `sin2x\in[-1;1]->0<=sin^2(2x)<=1`

`->1-3/4*1<=Q=1-3/4*sin^2(2x)<=1-3/4*0`

`->1/4<=Q<=1`

Vậy: `Q_(max)=1` khi `sin^2(2x)=0` và `Q_(min)=1/4` khi `sin^2(2x)=1`