1.证明下列题目：1.) sin78度+cos132度=sin18度2.) cos15度+sin15度/cos15度-s
1个回答
1（1）
sin78°+cos132°
＝sin78°－sin42°
＝2cos60°sin18°
＝sin18°
（2）
(cos15°＋sin15°)/(cos15°-sin15°)
＝(sin75°＋sin15°)/(sin75°-sin15°)
＝(2sin45°cos30°)/(2cos45°sin30°)
＝cot30°
＝√3
2、x+y+z =π
sin(x+y)=sin(π-z)=sinz
cos(x+y)=cos(π-z)=-cos z
sin2x+sin2y+sin2z
=2sin(x+y)cos(x-y)+sin2z
=2sinzcos(x-y)+2sinzcosz
=2sinz[cos(x-y)+cosz]
=(2sinz)×[2cos(x+z-y)/2][cos(x-y-z)/2]
=(4sinz)cos(π/2-y)cos(π/2-x)
=(4sinz)(siny)(sinx)
=4sinxsinysinz
3、sinx+sin(x+2π/3)+sin(x+4π/3)
＝sinx+2sin(x+π)cos(π/3)
＝sinx+(-sinx)
＝0
