Question

计算：

sin65°+sin15°sin10°

sin25°-cos15°cos80°

的值为 ______．

Answer 1

sin65°+sin15°sin10°

sin25°-cos15°cos80°

=

sin65°- 1 2 (cos25°-cos5° )

sin25°- 1 2 (cos95°+cos65° )

=

1 2 sin65°+ 1 2 cos5°

1 2 sin25°- 1 2 cos95°

=

cos25°+cos5°

cos65°-cos95°

=

2cos15°cos10°

2sin80°sin15°

=cot15°
=tan75°=2+

3

故答案为：2+

3