问题 解答题

求tan20°+4sin20°的值.

答案

tan20°+4sin20°=

sin20°+4sin20°cos20°
cos20°

=

sin20°+2sin40°
cos20°

=

(sin20°+sin40°)+sin40°
cos20°

=

2sin30°cos10°+sin40°
cos20°

=

sin80°+sin40°
cos20°
=
2sin60°cos20°
cos20°

=2sin60°=

3

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