If `f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+pi/3)` and `g(5/4)=1,`then `(gof)(x)`is ____________A. a polynomial of first degree in sin x and cos xB. a constant functionC. a polynomial of second degree in sin x and cos xD. none of these

If `f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+pi/3)` and `g(5/4)=1,`then `(g

1.	If `f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+pi/3)` and `g(5/4)=1,`then `(gof)(x)`is ____________A. a polynomial of first degree in sin x and cos xB. a constant functionC. a polynomial of second degree in sin x and cos xD. none of these
Answer» Correct Answer - B We have `f(x)=sin^(2)x+sin^(2)(x+(pi)/(3))+cos(x+(pi)/(3))cos x` `f(x)=(1)/(2){1-cos 2x+1-cos(2x+(2pi)/(3))+cos(2x+(pi)/(3))+"cos"(pi)/(3)}` `f(x)=(1)/(2)[(5)/(2)-{cos2x+cos(2x+(2pi)/(3)p)}+cos(2x+(pi)/(3))]` `Rightarrow f(x)=(1)/(2)[(5)/(2)-2cos(2x+(pi)/(3))"cos" (pi)/(3)+cos(2x+(pi)/(3))]` `f(x)=(5)/(4)"for all "x in R` `therefore "g of "(x)=g (f(x))=g((5)/(4))=1"for all x"` Hence, g of (x) is a constant functions.