Question 817705
cos(x+45)+cos(x-45)=radical 2
Identity: {{{cos(s)+cos(t)=2cos((s+t)/2)cos((s-t)/2)}}}
{{{cos(x+45)+cos(x-45)=2cos((x+45+x-45)/2)cos((x+45-x+45)/2)=sqrt(2)}}}
{{{2cos(2x/2)cos((90)/2)=sqrt(2)=2cos(x)cos(45)=sqrt(2)}}}
2cos(x)cos(45)=√2
2cos(x)(√2/2)=√2
cos(x)=√2/√2=1
x=0
..
Check:
cos(x+45)+cos(x-45)
=cos(45)+cos(-45)=cos(x+45)+cos(x-45)=√2/2+√2/2=2√2/2=√2