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Prove that `cos(pi/4-x) cos (pi/4+x)=1/2-sin^2x`

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Prove that `cos(pi/4-x) cos (pi/4+x)=1/2-sin^2x`
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`[cospi/4cosx+sinpi/4sinx][cospi/4cosx-sinpi/4sinx]`
`cos^2pi/4cos^2x-sin^2pi/4sin^2x`
`1/2(1-sin^2x)-1/2sin^2x`
`1/2-1/2sin^2x-1/2sin^2x`
`1/2-sin^2x`.
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