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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(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

Similar Questions

$\left( {1 + \cos \frac{\pi }{8}} \right)\,\left( {1 + \cos \frac{{3\pi }}{8}} \right)\,\left( {1 + \cos \frac{{5\pi }}{8}} \right)\,\left( {1 + \cos \frac{{7\pi }}{8}} \right) = $

The value of $\frac{\tan 40^{\circ}+\tan 20^{\circ}}{1-\cot 70^{\circ} \cot 50^{\circ}}$ is equal to

The minimum value of $2 \sin ^{2} \theta+3 \cos ^{2} \theta$ is

$\cos \frac{\pi }{5} \cos \frac{2\pi }{5} \cos \frac{4\pi }{5} \cos \frac{8\pi }{5} = $

Find the value of $\tan 4^{\circ} \tan 43^{\circ} \tan 47^{\circ} \tan 86^{\circ}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module