# Evaluating $sin 10^circ + sin 20^circ + sin 30^circ + cdots +sin 90^circ$

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?

Mathematics Asked by Crevious on December 31, 2020

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.

$$S = sin ( average; angle)cdot dfrac{sin n beta/2}{sin beta/2}$$

$$={ sin 50^{circ}}dfrac{ sin 9times 5^{circ}}{sin 5^{circ}}.$$

Correct answer by Narasimham on December 31, 2020

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