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1.æ示
sinï¼90°-aï¼=cosa
cosï¼180°-aï¼=-cosa
2.
âµa为第äºè±¡éè§,sina+cosa=ä¸åä¹æ ¹å·ä¸>0
â´Ï/2<a<3Ï/4
â´Ï<2a<3Ï/2
â´cos2aã0
âµsina+cosa=ä¸åä¹æ ¹å·ä¸
两侧平æ¹åæ´çå¾2sinacosa=-2/3
å³sin2a=-2/3
â´cos2a=-âï¼1-sin²2aï¼=-â5/3
3.æ示ï¼sin2a=2sinacosaï¼
= 2æ ¹å·(sin4+cos4)²+æ ¹å·2*2cos²4
=2|sin4+cos4|+2|cos4|
ç±äº
Ï<4<3Ï/2
æ以
sin4<0,cos4<0,sin4+cos4<0
æ以åå¼=-2(sin4+cos4)-2cos4=-2sin4-4cos4
4.
解ï¼
aæ¯éè§
Ï/2<a+Ï/6<2Ï/3
cos(a+Ï/6)=4/5,
sin(a+Ï/6)=3/5
sin(2a+Ï/3)=2sin(a+Ï/6)cos(a+Ï/6)=2*(4/5)*(3/5)=24/25
cos(2a+Ï/3)=2cos²(a+Ï/6)-1=2*(4/5)²-1=7/25
sin(2a+Ï/12)
=sin[(2a+Ï/3)-Ï/4]
=sin(2a+Ï/3)cos(Ï/4)-cos(2a+Ï/3)cos(Ï/4)
=(24/25)*(â2/2)-(7/25)*(â2/2)
=17â2/50
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