Question

化简

1+tan150

1-tan150

的值等于______．

Answer 1

∵

1+tan150

1-tan150

=

1+ sin15° cos15°

1- sin15° cos15°

=

sin15°+cos15°

cos15°-sin15°

=

(sin15°+cos15°)2

(cos15°-sin15°)(cos15°+sin15°)

=

1+sin30°

cos30°

=

3 2

3 2

=

3

．
故答案为：

3

．