Question

计算：

sin65°+sin15°sin10°

sin25°-cos15°cos80°

．

Answer 1

sin65°+sin15°sin10°

sin25°-cos15°cos80°

=

cos(10°+15°)+sin15°sin10°

sin(15°+10°)-cos15°sin10°

=

cos10°cos15°

sin15°cos10°

 
=

cos15°

sin15°

=

cos(45°-30°)

sin(45°-30°)

=

2 2 × 3 2 + 2 2 × 1 2

2 2 × 3 2 - 2 2 × 1 2

=

6 + 2

6 - 2

=2+

3

．