The value of sin 10^circ + sin 20^circ + sin | vedclass

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(B) The given expression is a sum of sines of angles in an arithmetic progression: $S = \sum_{k=1}^{36} \sin(k \cdot 10^\circ)$.Using the formula for

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(B) The given expression is a sum of sines of angles in an arithmetic progression: $S = \sum_{k=1}^{36} \sin(k \cdot 10^\circ)$.Using the formula for the sum of sines of angles in arithmetic progression: $\sum_{k=1}^{n} \sin(a + (k-1)d) = \frac{\sin(n d / 2)}{\sin(d / 2)} \cdot \sin\left(a + \frac{(n-1)d}{2}\right)$.Here,$a = 10^\circ$,$d = 10^\circ$,and $n = 36$.$S = \frac{\sin(36 \cdot 10^\circ / 2)}{\sin(10^\circ / 2)} \cdot \sin\left(10^\circ + \frac{35 \cdot 10^\circ}{2}\right)$.$S = \frac{\sin(180^\circ)}{\sin(5^\circ)} \cdot \sin(10^\circ + 175^\circ)$.Since $\sin(180^\circ) = 0$,the entire expression evaluates to $0$.

The value of $\sin 10^\circ + \sin 20^\circ + \sin 30^\circ + ... + \sin 360^\circ$ is

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