sin(π/16)^2-cos(π/16)^2

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sin(π/16)^2-cos(π/16)^2sin(π/16)^2-cos(π/16)^2sin(π/16)^2-cos(π/16)^2sin(π/16)^2-cos(π/16)^2=-cosπ/8

sin(π/16)^2-cos(π/16)^2
sin(π/16)^2-cos(π/16)^2

sin(π/16)^2-cos(π/16)^2
sin(π/16)^2-cos(π/16)^2
=-cosπ/8
=-√[(1+cosπ/4)/2]
=-√[(1+√2/2)/2]
=-√(2+√2)*1/2