题目内容

(1)化简:
(log25)2-4log25+4
 
+log2
1
5

(2)计算:tan70°cos10°(
3
tan20°-1)
(1)∵
(log25)2-4log25+4
 
=log25-2,
∴原式=log25-2+log2
1
5
=-2+log2(5×
1
5
)
=-2+log21=-2;
(2)原式=
sin70°cos10°
cos70°
3
sin20°-cos20°
cos20°

=
sin70°cos10°
cos70°
2sin(20°-30°)
cos20°

=-
2sin70°sin20°
cos70°cos20°

=-
2sin70°sin20°
sin20°sin70°

=-2.
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