化简cos^2（四分之兀-α）-sin^2（四分之兀-α）得到

题目

化简cos^2（四分之兀-α）-sin^2（四分之兀-α）得到

答案

cos^2（π/4-α）-sin^2（π/4-α）
={cos（π/4-α）+sin（π/4-α）} {cos（π/4-α）-sin（π/4-α) }
=根号2{cos π/4 cos（π/4-α）+sinπ/4 sin（π/4-α）} 根号2{cosπ/4 cos（π/4-α）-sinπ/4 sin（π/4-α) }
=2 cos[π/4-(π/4-α）] {cos[π/4+(π/4-α)]
=2 cosα cos(π/2-α)
=2 cosα sinα
=sin2α