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`

Explanation

`L.H.S. = sin^4((pi)/8)+sin^4((3pi)/8)+sin^4((5pi)/8)+sin^4((7pi)/8)`

`=sin^4((pi)/8)+sin^4((3pi)/8)+sin^4(pi-(3pi)/8)+sin^4(pi-(pi)/8)`

`=sin^4((pi)/8)+sin^4((3pi)/8)+sin^4((3pi)/8)+sin^4((pi)/8)...[As sin(pi-theta) = sintheta]`

`=2(sin^4((pi)/8)+sin^4((3pi)/8))`

`=2((sin^2((pi)/8))^2+(sin^2((3pi)/8))^2)`

`=2(((1-cos(pi/4))/2)^2+((1-cos((3pi)/4))/2)^2)`

`=2/4[(1-1/sqrt2)^2+(1+1/sqrt2)^2]`

`=1/2[1+1/2-sqrt2+1+1/2+sqrt2]`

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