Question

(cos pi/8 + sin pi/8)*(cos^3 pi/8 - sin^3 pi/8) =

Answer 1

$(cos( frac{pi}{8} )+sin(frac{pi}{8}))*(cos^3(frac{pi}{8})-sin^3(frac{pi}{8}))= \ =(cos( frac{pi}{8} )+sin(frac{pi}{8}))*(cos( frac{pi}{8} )-sin(frac{pi}{8}))*(cos^2( frac{pi}{8} )+sin^2(frac{pi}{8})+cos(frac{pi}{8})sin(frac{pi}{8})=$
$=(cos^2( frac{pi}{8} )-sin^2(frac{pi}{8} )) * (1+ frac{sin( frac{pi}{4} )}{2} )=\ =(cos( frac{pi}{4} ))*(1+ frac{1}{2 sqrt{2} } )= frac{2 sqrt{2} +1}{4}$