prove that `cos^2(pi/8)+cos^2((3pi)/8)+cos^2((5pi)/8)+cos^2((7pi)/8)=2`

Prove that cos^(4)pi/8+cos^(4)(3pi)/(8)+cos^(4)(5pi)/8+cos^(4)(7pi)/8=3/2

Prove that cos((pi)/(8))+cos((3 pi)/(8))+cos((5 pi)/(8))+cos((7 pi)/(8))=0

Prove that cos((2pi)/7) cos((4pi)/7) cos((8pi)/7) =1/8

Prove that cos((2pi)/7)cos((4pi)/7)cos((8pi)/7)=1/8

Statement I : sin^2pi/8+sin^2(3pi)/8+sin^2(5pi)/8+sin^2(7pi)/8=2 Statement II cos^2pi/8+cos^2(3pi )/8+cos^2(5pi)/8+cos^2(7pi/8)=2 Statement III: sin^2pi/8+sin^(3pi)/8+sin^2(5pi)/8sin^2 (7pi)/8=3/2

Prove that: cos^(4)(pi)/(8)+cos^(4)(3 pi)/(8)+cos^(4)(5 pi)/(8)+cos^(4)(7 pi)/(8)=(3)/(2)

Prove that (1 + cos(pi/8))(1 + cos(3pi/8))(1 + cos(5pi/8))(1 + cos(7pi/8)) = 1/8

Prove that: sin^(2)pi/8+sin^(2)(3pi)/(8)+sin^(2)(5pi)/8+sin^(2)(7pi)/8=2

Prove that: sin((3pi)/(8)-5)cos((pi)/(8)+5)+cos((3pi)/(8)-5)sin((pi)/(8)+7)=1