# The value of (1+cos pi/8)(1+cos 3pi/8)(1+cos 5pi/8)(1+cos 7pi /8)is

Solution: We have,

$\\ cos 5\pi /8=cos(\pi -3\pi /8)=-cos3\pi /8;And;cos7\pi /8=cos(\pi -\pi /8)=cos\pi /8\\ \\ \therefore E=(1-cos^2\pi /8)(1-cos^23\pi /8)=sin^2\pi /8\times sin^23\pi/8=1/4(2sin\pi /8\times sin3\pi /8)^2=1/4(cos\pi /4-cos\pi /2)^2=1/8$

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