What is the maximum value of 1+8(sin^2×x^2×cos^2×x^2)

9 can be maximum value of the function.Since the sin(x) and cos(x) lies between -1 and 1.It could be:=1+8(1 X 1)=1+8=9

Sinx,cosx have the values between -1,+1Then sin^2x,cos^2x will have values 0,1Then put sin^2x and cos ^x 1Let,`s do = 1+8(1×1×1×1) = 1+8 =9

=1+8(sin^2x^2cos^2x^2)=1+2(4sin^2x^2cos^2x^2)=1+2(2sinx^2cosx^2)^2 [2sinx^2cisx^2 is in the form of 2sinAcosB => sin(A+B)-sin(A-B) = sin(2x^2)-sin(0) = sin2x^2]=1+2(sin(2x^2))^2 = 1+2sin^2×2x^2[cos2A=1-2sin^2×A => 2sin^2×x^2=cos4x^2-1]=1+cos4x^2-1=2-cos4x^2Maximum value (General form = asinx+bcosx+c) => c+ root over a^2+b^2=here; in 2-cos4x^2; a=1, b=0, c=2If we calculate using maximum value formula we get [ 3 ]