quantaviousw49
29.07.2019 •
Mathematics
Siplifier cos(π/7)+cos(2π/7)+cos(3π/7)+cos(4π/7)
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Ответ:
cos a+cos b=cos[(a+b)/2]*cos[(a-b)/2]
we have
cos(π/7)+cos(2π/7)+cos(3π/7)+cos(4π/7)> equation 1
cos(4π/7)+cos(2π/7)=cos[(4π/7+2π/7)/2]*cos[(4π/7-2π/7)/2]
=cos(3π/7)*cos(π/7)
then
cos(4π/7)+cos(2π/7)=cos(3π/7)*cos(π/7)> equation 2
[cos(3π/7)+cos(π/7)]=cos[(3π/7+π/7)/2]*cos[(3π/7-π/7)/2]
=cos(2π/7)*cos(π/7)
then
[cos(3π/7)+cos(π/7)]=cos(2π/7)*cos(π/7)> equation 3
I substitute 2 and 3 in 1
[cos(3π/7)+cos(π/7)]+[cos(4π/7)+cos(2π/7)]
{cos(2π/7)*cos(π/7}+{cos(3π/7)*cos(π/7)}
=cos(π/7)*[cos(2π/7)+cos(3π/7)]
the answer is
cos(π/7)+cos(2π/7)+cos(3π/7)+cos(4π/7)=cos(π/7)*[cos(2π/7)+cos(3π/7)]
Ответ:
Its a good probability
Step-by-step explanation: