cos负25π/12等于多少?

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cos负25π/12等于多少?
cos负25π/12等于多少?

cos负25π/12等于多少?
cos(-25π/12)
= cos(25π/12)
= cos(2π+π/12)
= cos(π/12)
= cos{(π/6)/2}
= √{[1+cos(π/6)]/2}
= √{[1+√3/2]/2}
= √(2+√3)/2
= (√3+1)/(2√2)
= (√6+√2)/4

cos(-25π/12)=cos(25π/12)=cos(2π+π/12)=cos(π/12)=根号[(cos(2*π/12)+1)/2]
=根号[((根号3)/2+1)/2]
=根号[((根号3)+2)/4]
=根号[((根号3)+2)]/2
=0.9659258262890682867497431997289

诱导公式
cos(-25pi/12)=cos(25pi/12)
=cos(2pi+pi/12)
=cos(pi/12)>0
由于cos(pi/6)=2(cos(pi/12))^2-1 (二倍角公式）=根3/2
解得cos(-25pi/12)=cos(pi/12)=根（1+根3）/2

cos(-25π/12)=cos(25π/12)=cos(2π+π/12)=cos(π/12)=cos(π/4-π/6)=(√6+√2)/4（此处是用两角和的余弦展开算的，自己算吧）

=cos(-2π-π/12)=cosπ/12
=根号[(1/2+根号3/4)]

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