The question is finding $$S = \sin 10^\circ + \sin 20^\circ + \sin 30^\circ + \cdots +\sin 90^\circ$$
I tried to do it, but I can't eliminate the $\cos 5^\circ$.
Can anyone help me with the answer?
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1Why do you want to eliminate $\cos 5^\circ$? – Angina Seng Oct 06 '20 at 08:53
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2Use https://math.stackexchange.com/questions/17966/how-can-we-sum-up-sin-and-cos-series-when-the-angles-are-in-arithmetic-pro – lab bhattacharjee Oct 06 '20 at 08:54
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@AnginaSneg That for finding the ans easily . If you know any altenative method please show me . – Crevious Oct 06 '20 at 08:58
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Best it is to follow symbolic derivation of sums of sine of $n$ angles in A.P, of common difference $\beta= 10^{\circ}.$ And then apply it.
$$ S = \sin ( average\; angle)\cdot \dfrac{\sin n \beta/2}{\sin \beta/2}$$
$$={ \sin 50^{\circ}}\dfrac{ \sin 9\times 5^{\circ}}{\sin 5^{\circ}}.$$
Narasimham
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