Question

1+tan75°1?tan75°的值等于______

1+tan75°1?tan75°的值等于______．

Answer 1

1+tan75°

1?tan75°

=

tan45°+tan75°

1?tan45°?tan75°

=tan（45°+75°）=tan120°=-tan60°=-

3

，
故答案为-

3

．

Answer 2

1+tan75°/1-tan75°=tan(45度+75度）=tan120度=-根号3

Answer 3

1+tan75°/1-tan75°
其实=(
tan45°+tan75°)
/
(1-tan45°
*
tan75°
)
=
1+tan75°/1-tan75°
(tan45°为1)
=
tan
(45°
+
75°)
=
tan
(120°)
=
--√3

Answer 4

1+tan75°/1-tan75°
=(sin75°+cos75°)/(cos75°-sin75°)
=(sin75°+sin15°)/(sin15°-sin75°)
=2sin45°cos30°/(-2sin30°cos45°)
=-cos30°/sin30°
=-(√3/2)/(1/2)
=-√3