高三数学函数问题

Question

1.sin163°*sin223°+sin253°*sin313°2.sin 7π/18  * cos 2π/9 -sin π/9 *sin 2π/9 3.(1+tan22°）*（1+tan23°）4.cos π/9 *cos 2π/9 * cos 3π/9 * cos 4π/9要具体解答过程。 拜托各位高手~

Answer 1

1.sin163°*sin223°+sin253°*sin313°
=sin(180°-17°)sin(180°+43°)+sin(180°+73°)sin(360°-47°)
=-sin17°sin43°+sin73°sin47°
=-sin17°sin43°+cos17°cos43°
=cos(43°+17°)
=1/2

2.sin 7π/18 * cos 2π/9 -sin π/9 *sin 2π/9
=cosπ/9 * cos 2π/9 -sin π/9 *sin 2π/9
=-cos(2π/9+π/9)
=-1/2
3.(1+tan22°）*（1+tan23°）
=1+( tan22° +tan23°)+ tan22°tan23°
=1+tan45°(1- tan22°tan23°) + tan22°tan23°
=2
4.cos π/9 *cos 2π/9 * cos 3π/9 * cos 4π/9
= 1/4*[2sinπ/9cos π/9 cos 2π/9 cos 4π/9]/sinπ/9
=1/4 * [sin2π/9cos 2π/9 cos 4π/9]/sinπ/9
=1/8 * [sin4π/9 cos 4π/9]/sinπ/9
=1/16 * [sin8π/9]/sinπ/9
=1/16