Question

sin50(1+根号3tan10)求解，多种方法

Answer 1

【1】
1+(√3)tan10
=1+(√3)[sin10/cos10] (∵tan10=sin10/cos10 )
=[2/cos10]×[(1/2)cos10+(√3/2)sin10]
=[2/cos10]×[sin30cos10+cos30sin10]
=[2/cos10]sin40. (∵sin40=sin(30+10)=sin30cos10+cos10sin30]
=(2cos50)/cos10. (∵sin40=sin[90-50]=cos50. )
【2】
原式
=（2sin50cos50)/cos10
=(sin100)/cos10
=cos10/cos10
=1

Answer 2

【1】
1+(√3)tan10
=1+(√3)[sin10/cos10] (∵tan10=sin10/cos10 )
=[2/cos10]×[(1/2)cos10+(√3/2)sin10]
=[2/cos10]×[sin30cos10+cos30sin10]
=[2/cos10]sin40. (∵sin40=sin(30+10)=sin30cos10+cos10sin30]
=(2cos50)/cos10. (∵sin40=sin[90-50]=cos50. )
【2】
原式
=（2sin50cos50)/cos10
=(sin100)/cos10
=cos10/cos10
=1

Answer 3

sin50(1+√3tan10)=sin50(1+tan(60)tan10))=sin50(1+sin(60)sin10)/[cos(60)cos(10])=sin(50)[sin60sin10+cos60cos10]/[cos60cos10]=sin(50)cos(60-10)/[cos(60)cos(10)]=sin(50)cos(50)/[cos(60)cos(10)]=sin(100)/[2cos(60)cos(10)]=sin(100)/cos(10)=cos(10)/cos(10)=1
(1+√3tan10)=(-cos120cos10+sin120sin10)*2/cos10=-2cos130/cos10=2cos50/cos10
sin50*(1+√3tan10)=(2sin50cos50)/cos10=sin100/cos10=sin80/cos10=cos10/cos10=1

Answer 4

=SIN(50*PI()/180)*(1+SQRT(3)*TAN(10*PI()/180))=1