Question

sin5 +sin10..............+sin180
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Answer 1

HI FRND

Let

a=sin5°+sin10°+sin15°+⋯+sin40°=Im(∑n=08exp(in5π/180))a=sin⁡5°+sin⁡10°+sin⁡15°+⋯+sin⁡40°=Im⁡(∑n=08exp⁡(in5π/180))

and

b=sin5°+sin10°+sin15°+⋯+sin175°=Im((1+exp(i9⋅5π/180)+exp(i2⋅9⋅5π/180)+exp(i3⋅9⋅5π/180))⋅∑n=08exp(in5π/180))=Im((1+exp(iπ/4)+exp(i2π/4)+exp(i3π/4))⋅∑n=08exp