Question

求cos80°sin70°+sin80°sin20°的值

Answer 1

解1：
cos80°sin70°+sin80°sin20°
=cos80°sin(90°-20°)+sin80°sin20
=cos80°cos20°+sin80°sin20°
=cos(80°-20°)
=cos60°
=1/2

解2：
cos80°sin70°+sin80°sin20°
=cos80°sin70°+sin80°sin(90°-70°)
=cos80°sin70°+sin80°cos70°
=sin70°cos80°+cos70°sin80°
=sin(70°+80°)
=sin150°
=sin(180°-30°)
=sin30°
=1/2

Answer 2

cos80°sin70°+sin80°sin20°
=cos80°sin70°+sin80°cos70°
=sin(70°+80°)
=sin150°
=sin30°
=1/2

追问

若逆用两角和与差的余弦公式,怎么作?

追答

cos80°sin70°+sin80°sin20°
=cos80°cos20°+sin80°sin20°
=cos(80°-20°)
=cos60°
=1/2