1-2cos^2(π/4-a/2)

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1-2cos^2(π/4-a/2)
1-2cos^2(π/4-a/2)

1-2cos^2(π/4-a/2)
1-2cos^2(π/4-a/2)
=1-2sin^2(π/2-(π/4-a/2))
=1-2sin^2(π/4+a/2)
=cos(2(π/4+a/2))
=cos(π/2+a)
=-sina

1-2cos^2(π/4-a/2)
=cos[2*(π/4-a/2)]
=cos(π/2-a)
=sin(a)

1-2cos^2(π/4-a/2)=-[2cos^2(π/4-a/2)-1]
=-cos2(π/4-a/2)=-cos(π/2-a)=-sina