The general solution of the equation 1+sinx+....+sinnx+.....1−sinx+....+−1nsinnx+....=1−cos2x1+cos2x ,  x≠2n+1π/2,n∈I is

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-π6x=nπ+(−1)n+1π6