Question

数学题化简

sin347cos148 sin77cos58和sin164sin224 sin254sin314

Answer 1

sin347°cos148°+sin77°cos58°
=sin(360°-13°)cos(180°-32°)+cos13°sin32°
=sin13°cos32°+cos13°sin32°
=sin(13+32)°
=sin45°
=根号2/2

sin164°sin224°+sin254°sin314°
=sin16°(-sin44°)+(-sin74°)(-sin46°)
=sin74°sin46°-sin16°sin44°
=sin74°cos44°-cos74°sin44°
=sin(74°-44°)
=sin30°
=1/2

Answer 2

sin347cos148+sin77cos58
=sin(360-13)cos(180-32)+sin(90-13)cos(90-32)
=(-sin13)(-cos32)+cos13sin32
=sin13cos32+cos13sin32
=sin(13+32)
=sin45
=√2/2

sin164sin224+sin254sin314
=sin(180-16)sin(180+44)+sin(270-16)sin(270+44)
=sin16(-sin44)+(-cos16)(-cos44)
=cos16cos44-sin16sin44
=cos(16+44)
=cos60
=1/2

Answer 3

　　(1)sin347°cos148°+ sin77°cos58°
　　=sin(360°-13°)cos(180°-32°)+ sin(90°-13°)cos58°
　　=-sin13°(-cos32°)+ cos13°cos58°
　　=sin13°cos32°+ cos13°cos(90°-32°)
　　=sin13°cos32°+ cos13°sin32°
　　=sin45°
　　=√2/2
　　(2)sin164°sin224°+sin254°sin314°
　　=sin(180°-16°)sin(180°+44°)+sin(270°-16°)sin(270°+44°)
=sin16°(-sin44°)+(-cos16°)(-cos44°)
=cos16°cos44°-sin16°sin44°=cos(16°+44°)
=cos60°
　　=1/2