Use the half-angle formulas to simplify the expression.

The simplified answer is: −sin(x−12) 

\(cos(2*13x)=cos^2(13x)-sin^2(13x)\\ cos(2*13x)=cos^2(13x)-(1-cos^2(13x))\\ cos(2*13x)=2cos^2(13x)-1\\ \frac{cos(2*13x)+1}{2}=cos^2(13x)\\ so\\ \frac{1+cos(26x)}{2}=cos^2(13x)\\ \sqrt{\frac{1+cos(26x)}{2}}=\sqrt{cos^2(13x)}\\ \sqrt{\frac{1+cos(26x)}{2}}=cos(13x)\\ where \quad cos(13x) \ge 0\)