Question

Sinα-sin(120-α)+sin(120+α)
1) 1/2 2)1 3)3/2 4)0

Answer 1

Answer:

$\rm 0$

Step-by-step explanation:

We have,

$\tt \sin \alpha - \sin (120- \alpha) + \sin (120+ \alpha)$

$\rm \sin \alpha - \sin (90^{\circ}+30^{\circ}- \alpha) + \sin (90^{\circ}+30^{\circ}+ \alpha)$

$\rm \sin \alpha - \cos (30^{\circ}- \alpha) + \cos (30^{\circ}+ \alpha)$

$\rm \sin \alpha - \cos 30^{\circ} \cos \alpha - \sin 30^{\circ} \sin \alpha + \cos 30^{\circ} \cos \alpha - \sin 30^{\circ} \sin \alpha$

$\rm \sin \alpha - \cancel{\cos 30^{\circ} \cos \alpha} - \sin 30^{\circ} \sin \alpha + \cancel{\cos 30^{\circ} \cos \alpha} - \sin 30^{\circ} \sin \alpha$

$\rm \sin \alpha - 2 \sin 30^{\circ} \sin \alpha$

$\rm \sin \alpha - \cancel{2} \times \dfrac{1}{\cancel{2}} \sin \alpha$

$\rm \sin \alpha - \sin \alpha$

$\rm =0$