Question

solve :-

sin D+ sin 2D + sin 3D ........till n terms

Answer 1

@goformit100 ....we can use fourier transform ???

Answer 2

How ?

Answer 3

Let S=sin D+sin 2D+ sin 3D+... nterms
C=cosD+cos2D+cos 3D+...n ~terms
\[C+\iota S=e ^{\iota D}+e ^{2 \iota D}+e ^{3\iota D}+... n~terms.\]
\[=\frac{ e ^{\iota D}\left( e ^{\iota n D}-1 \right) }{e ^{\iota D}-1 }\]
write \[e ^{\iota D}=CosD+\iota Sin D\]
and \[e ^{\iota n D}=Cos~ n D+\iota~ Sin~ n D\]
then rationalise and in the end equate imaginary parts.