化简cos2(π/4-α)-sin2(π/4-α)
问题描述：
化简cos2(π/4-α)-sin2(π/4-α)
cos^2(π/4-α)-sin^2(π/4-α)
答
cos2(π/4-α)-sin2(π/4-α)
=cos(π/2-2α）-sin(π/2-2α)
=sin2α-cos2α
=√2(√2/2sin2α-cos2α)
=√2sin(2α-π/4)
根据二倍角公式
cos2α=cos²α-sin²α
∴cos²(π/4-α)-sin²(π/4-α)
=cos[2(π/4-α)]
=cos(π/2-2α)
=sin2α