cos(π/6-α)=m,m绝对值小于等于1,求cos(5π/6+α)

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cos(π/6-α)=m,m绝对值小于等于1,求cos(5π/6+α)
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cos(π/6-α)=m,m绝对值小于等于1,求cos(5π/6+α)
cos(π/6-α)=m,m绝对值小于等于1,求cos(5π/6+α)

cos(π/6-α)=m,m绝对值小于等于1,求cos(5π/6+α)
cos(5π/6+α)=-cos[π-(5π/6+α)]=-cos(π/6-α)
所以cos(5π/6+α)=-m

cos(5π/6+α)=cos[π-(π/6-α)]
=cosπcos(π/6-α)+sinπsin(π/6-α)
=-1*m+0*根号下1-m2
=-m

cos(π/6-α)=cos[π-(5π/6+α)]=-cos(5π/6+α)
所以cos(5π/6+α)=-m
记住奇变偶不变 符号看象限

cosπ=-1
=cos[(π/6-a)+(5π/6+a)]
=cos(π/6-a)cos(5π/6+a)-sin(π/6-a)sin(5π/6+a)
=mcos(5π/6+a)-根号(1-m^2)根号mcos(5π/6+a)
设mcos(5π/6+a)=x
mx-根号(1-m^2)根号1-x^2
=-1
解出x=-m

cos(5π/6+α)=cos[π-(π/6-α)]=-cos[-(π/6-α)]
=-cos(π/6-α)=-m