If f(x)=sin2x + sin2(x+pi/3)+ cosx*cos(x+pi/3), and g(5/4)=1 then find gof(x) - Maths - Relations and Functions

Question

If f(x)=sin2x + sin2(x+pi/3)+
cosx*cos(x+pi/3), and g(5/4)=1 then find gof(x)

Lovina Kansal · Accepted Answer

Dear student

We have,f(x)=sin2x+sin2x+π3+cosx cosx+π3⇒f(x)=122sin2x+2sin2x+π3+2cosx cosx+π3⇒f(x)=121-cos2x+1-cos2x+2π3+cos2x+π3+cosπ3⇒f(x)=1252-cos2x-cos2x+2π3+cos2x+π3⇒f(x)=1252-cos2x+cos2x+2π3+cos2x+π3⇒f(x)=1252-2cos2x+π3cosπ3+cos2x+π3⇒f(x)=1252-cos2x+π3+cos2x+π3⇒f(x)=54 for all x∈RTherefore, for any x∈R, we havegof(x)=gfx=g54=1Thus, gof(x)=1 for all x∈RHence, gof:R→R is a constant function
 
Regards