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) Let $S = \sum_{k=1}^{36} \sin(k 	imes 10^\circ)$.We know that $\sin(180^\circ + 	heta) = -\sin 	heta$.Thus,$\sin(180^\circ + 10^\circ) = \sin 1

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(B) Let $S = \sum_{k=1}^{36} \sin(k 	imes 10^\circ)$.We know that $\sin(180^\circ + 	heta) = -\sin 	heta$.Thus,$\sin(180^\circ + 10^\circ) = \sin 190^\circ = -\sin 10^\circ$.Similarly,$\sin(180^\circ + 20^\circ) = \sin 200^\circ = -\sin 20^\circ$,and so on up to $\sin(180^\circ + 170^\circ) = \sin 350^\circ = -\sin 170^\circ$.Also,$\sin 180^\circ = 0$ and $\sin 360^\circ = 0$.The sum can be written as $(\sin 10^\circ + \sin 190^\circ) + (\sin 20^\circ + \sin 200^\circ) + \dots + (\sin 170^\circ + \sin 350^\circ) + \sin 180^\circ + \sin 360^\circ$.Since each pair sums to $0$ and $\sin 180^\circ = \sin 360^\circ = 0$,the total sum is $0$.

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

Similar Questions

If $\cos \theta - \sin \theta = \sqrt{5} \sin \theta$,then $\cos \theta + \sin \theta = $

If $\tan \theta + \cot \theta = 2$,then $\sin \theta$ is equal to

The value of $\frac{1}{4} \tan \frac{\pi}{8} + \frac{1}{8} \tan \frac{\pi}{16} + \frac{1}{16} \tan \frac{\pi}{32} + \dots \infty$ terms is equal to-

The equation $y = \sin \,x \sin \,(x + 2) - \sin^2 \,(x + 1)$ represents a straight line lying in

If $\tan A + \cot A = 4$,then $\tan^4 A + \cot^4 A$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module