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Sinx + sin2x = 1

2 sin 3x/2 cos x/2 = 1

cos x/2 = 1 / (2 sin 3x/2 )

cos x + cos 2x = 2 cos x/2 cos 3x/2 substitute value of cos x/2 from above

= cos 3x/2 / sin 3x/2 =

2 sin 3x/2 cos x/2 = 1

cos x/2 = 1 / (2 sin 3x/2 )

cos x + cos 2x = 2 cos x/2 cos 3x/2 substitute value of cos x/2 from above

= cos 3x/2 / sin 3x/2 =

__COT 3x/2__