[tex]\cos^2\dfrac{7\pi}8=\dfrac12\left(1+\cos\dfrac{7\pi}4\right)[/tex]
[tex]=\dfrac12+\dfrac12\cos\left(-\dfrac\pi4\right)[/tex]
[tex]=\dfrac12+\dfrac12\cos\dfrac\pi4[/tex]
[tex]=\dfrac12+\dfrac1{2\sqrt2}[/tex]
[tex]=\dfrac{\sqrt2+1}{2\sqrt2}[/tex]
[tex]=\dfrac{2+\sqrt2}4[/tex]
