Prove that `8pi-(8+4pi)=4pi-8`

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Prove that int_(pi/8)^(3 pi/8)(tan^(2)x backslash dx)/(tan^(2)x+cot^(2)x)=(pi)/(8)

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

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

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

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

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

4.Prove that sin^(2)((pi)/(8))+sin^(2)((3 pi)/(8))=1

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

Prove that cos(2 pi)/(15)cos(4 pi)/(15)cos(8 pi)/(15)cos(14 pi)/(15)=(1)/(16)