Question

求值：

2sin50°+sin80°(1+ 3 tan10°)

1+cos10°

．

Answer 1

原式=

2sin50°+ 2sin80° cos10° ( 1 2 cos10°+ 3 2 sin10°)

2 cos5°

=

2sin50°+ 2sin80° cos10° cos(60°-10°)

2 cos5°

=

2( 2 2 sin50°+ 2 2 cos50°)

cos5°

=

2cos(50°-45°)

cos5°

=2．