原式=[2sin50°+sin10°（1+

3 sin10°

cos10°

）]

1+cos20°

=（2sin50°+sin10°•

cos10°+ 3 sin10°

cos10°

）

1+cos20°

=（2sin50°+2sin10°•

sin(10°+30°)

cos10°

）

1+cos20°

=

2sin50°cos10°+2sin10°sin40°

cos10°

•

1+cos20°

=2cos（40°-10°）•

2 cos10°

cos10°

=2cos30°×

2

=

6

．