问题 填空题
1
tan70°
+4cos70°
的值是______.
答案

1
tan70°
+4cos70°=
cos70°
sin70°
+4cos70°=
cos70°+4sin70°cos70°
sin70°

=

cos70°+2sin140°
sin70°
=
cos70°+2sin40°
sin70°
=
cos70°+2sin(70°-30°)
sin70°

=

cos70°+2sin70°cos30°-2cos70°•sin30°
sin70°

=

2sin70°•cos30°
sin70°

=2cos30°=

3

故答案为:

3

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