若a属于【0,π/4】,y=log2(1+cos(9/2π-a))+log2(1+sin(a-5π))的值域为

问题描述:

若a属于【0,π/4】,y=log2(1+cos(9/2π-a))+log2(1+sin(a-5π))的值域为

y=log2(1+cos(9/2π-a))+log2(1+sin(a-5π))
=log2[(1+cos(π/2-a))((1+sin(a-π)]
=log2[(1+sina)(1-sina)]
=log2(cos^2a)
=2log2|cosa|
a属于【0,π/4】,根号2/2=cosa=1
-1/2=log2cosa=0
-1=2log2|cosa|=0