Question

sin50°-sin70°+sin10°....evaluate

Answer 1

HELLO THERE!

Here, we need to use the formula:

$sin C + sin D = 2sin\frac{C+D}{2}\times cos\frac{C-D}{2}$

Given,

$sin 50 - sin 70 + sin 10\\\\= sin 50 + sin 10 - sin 70\\\\= 2 sin \frac{50 + 10}{2}\times cos\frac{50-10}{2}-sin70\\\\= 2 sin 30 cos 20 - sin 70\\\\= 2 \times \frac{1}{2} cos 20 - sin 70\\\\= cos 20 - sin 70\\\\= cos 20 - sin (90 - 20)\\\\= cos 20 - cos 20\\\\= 0$

HOPE THIS HELPS..

Thanks!!