Answer:
cos(x=pi/4)= [tex]\frac{17}{26}*\sqrt{2}[/tex]
Step-by-step explanation:
Remember that [tex]sin^{2}(x) +cos^{2}(x)=1[/tex]
We need to find cos(x) from the above equation.
cos(x)= 12) / 13. This solution is positive since cos(x) in the range (2pi/3, 2pi) is positive.
Now, to obtain cos(x+pi/4) lets use the relation for cos(a+b)= cos(a)*cos(b)-sin(a)*sin(b)
where a=x, b =pi/4
Hence
cos(x+pi/4) =cos(x)*cos(pi/4) - sin(x)*sin(pi/4)
cos(x+pi/4) = [tex]\frac{\sqrt{2}}{2} * (cos(x)+5/13)[/tex]
cos(x=pi/4)=[tex]\frac{\sqrt{2} }{2} *(\frac{12}{13}+\frac{5}{13})=\frac{17}{26} \sqrt{2}[/tex]
