Value of cos 2*pi/7+cos 4*pi/7+cos 6*pi/7+cos 7*pi/7
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use formula of
cosA+cos(A+B)+cos(A+2B)+......+cos(A+(n-1)B)
= cos(A+(n-1)B/2)sin(nB/2)cosec(B/2)
so in question
A=2π/7
B=2π/7
n=4
ans =
cos(4π/7)sin(4π/7)÷sin(π/7)
cosA+cos(A+B)+cos(A+2B)+......+cos(A+(n-1)B)
= cos(A+(n-1)B/2)sin(nB/2)cosec(B/2)
so in question
A=2π/7
B=2π/7
n=4
ans =
cos(4π/7)sin(4π/7)÷sin(π/7)
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