求值:2sin50°+sin80°(1+3tan10°)1+cos10°.
问题描述:
求值:
. 2sin50°+sin80°(1+
tan10°)
3
1+cos10°
答
原式=
2sin50°+
(2sin80° cos10°
cos10°+1 2
sin10°)
3
2
cos5°
2
=
2sin50°+
cos(60°−10°)2sin80° cos10°
cos5°
2
=
2(
sin50°+
2
2
cos50°)
2
2 cos5°
=
=2.2cos(50°−45°) cos5°