x趋于0时,a(1-(cosx)^2)与x^2是等价无穷小,则a=?.请问怎么算

x趋于0时,a(1-(cosx)^2)与x^2是等价无穷小,则a=?.请问怎么算
x趋于0时,a(1-(cosx)^2)与x^2是等价无穷小,则a=?.请问怎么算

x趋于0时,a(1-(cosx)^2)与x^2是等价无穷小,则a=?.请问怎么算
1-(cosx)^2=(sinx)^2
a(sinx)^2/x^2
=a(sinx/x)^2
x趋于0则sinx/x极限是1
而等价无穷小则a(sinx/x)^2极限是1
所以a*1^2=1
a=1