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如果不使用洛氏定律的话，可以用一个变量变换，y=x-π/4. 将x->π/4, 变y->0 来求的
变量变换后，则极限式变为:
lim{sin2(y+π/4) - cos2(y+π/4)-1}/{cos(y+π/4) -sin(y+π/4}|y ->0
= lim {[sin2y*cos(π/2)+cos2y*sin(π/2)] - [cos2y*cos(π/2)-sin2y*sin(π/2)] -1}/[-(√2)(siny)]
=lim{cos2y+sin2y-1}/[(√2)(-siny)]
=lim {1- 2(siny)^2+2siny*cosy -1}/[-(√2)siny]
=lim{2siny[cosy-siny]/[-(√2)siny]
=lim{-(√2)[cosy-siny]}|y->0
=-(√2)
变量变换后，则极限式变为:
lim{sin2(y+π/4) - cos2(y+π/4)-1}/{cos(y+π/4) -sin(y+π/4}|y ->0
= lim {[sin2y*cos(π/2)+cos2y*sin(π/2)] - [cos2y*cos(π/2)-sin2y*sin(π/2)] -1}/[-(√2)(siny)]
=lim{cos2y+sin2y-1}/[(√2)(-siny)]
=lim {1- 2(siny)^2+2siny*cosy -1}/[-(√2)siny]
=lim{2siny[cosy-siny]/[-(√2)siny]
=lim{-(√2)[cosy-siny]}|y->0
=-(√2)
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