The general solution of the equation 1+sinx+....+sinnx+.....1−sinx+....+−1nsinnx+....=1−cos2x1+cos2x , x≠2n+1π/2,n∈I is
−1nπ/3+nπ
−1nπ/6+nπ
−1n+1π/6+nπ
−1n−1π/3+nπ
The equation 1+sinx+....+sinnx+.....1−sinx+....+−1nsinnx+....=1−cos2x1+cos2x
⇒1+sinx1−sinx=2sin2x2cos2x
⇒1+sinx2cos2x=sin2xcos2x
⇒1+sinx2=sin2x
⇒1+2sinx=0
⇒sinx=−12=sin-π6
x=nπ+(−1)n+1π6