Question

Find the function value of cos^2 (7pi/8)

Answer 1

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