Question

已知sin(x-3π/4)cos(x-π/4)=-1/4,求cos4x.

Answer 1

∵sin(x-3π/4)cos(x-π/4)=-1/4

==>[sin((x-3π/4)+(x-π/4))+sin((x-3π/4)-(x-π/4))]/2=-1/4 (应用正弦积化和差公式)

==>sin(2x-π)+sin(-π/2)=-1/2

==>-sin(2x)-1=-1/2

==>sin(2x)=-1/2

∴cos(4x)=1-2sin²(2x) （应用余弦倍角公式）

=1-2(-1/2)²

=1/2