lượng giác thi thử đại học

L

lovelycat_handoi95

[tex]\blue{DK:cos(5x) \not=0\\ 1+4\cos(x)\cos(3x)=\tan(5x)\\\Leftrightarrow \cos(5x)+4\cos(x)\cos(3x)\cos(5x)=\sin(5x)\\ \Leftrightarrow \cos(5x)+2\cos(3x)[\cos(6x)+\cos(4x)]=\sin(5x)\\\Leftrightarrow \cos(x)+2\cos(3x)\cos(6x)+2\cos(3x)\cos(4x)=\sin(5 x)\\\Leftrightarrow \cos(x)+\cos(3x)+\cos(5x)+\cos(7x)+\cos(9x)=\sin(5 x)\\ \Leftrightarrow sinx[\cos(x)+\cos(3x)+\cos(5x)+\cos(7x)+\cos(9x)]=\sin(5 x)sin(x)(sinx \not=0 )\\\Leftrightarrow \frac{1}{2}[sin(2x)+sin(4x)-sin(2x)+\sin(6x)-\sin(4x)+\sin(8x)-\sin(6x)+\sin(10x)-\sin(8x)]=sin(5x).sin(x)\\\Leftrightarrow sin(5x)cos(5x)=sin(5x)sin(x)\\ \Leftrightarrow \left[sin(5x)=0\\cos(5x)=sin(x)[/tex]
 
Last edited by a moderator:
B

buitrung2002

Dk cos5xkhax 0
sinx=0 khôg la nghiệm nhân 2vê cho sinx <=> sinx.cos5x+sin5x.cos5x-sinx.cos5x=sin5x.sinx
<=> sin5x.cos5x-sin5x.sinx=0
<=> sin5x(cos5x-sinx)=0
đến đây la pt tích.
11a1 THPT TÂN LƯỢC
 
Last edited by a moderator:
You must log in or register to reply here.
Top Bottom