Question

✓ 3
sin x sin (x + 30° ) + cos x sin (x +120° ) = 2​

Answer 1

Answer:

$\bf\huge\red{\mid{\overline{\underline{AnswEr}}}\mid}$

$sin(x + 60) + sin(x + 120)$

$= 2.sin  \frac{(x + 60)(x + 120)}{2} .cos \frac{(x + 60) - (x + 120)}{2}$

$= 2.sin \frac{2x + 180}{2} .cos \frac{ - 60}{2}$

$= 2.sin \: (90 + x).cos(30)$

$= 2.sin \: {90 - ( - x)} .cos \: 30$

$= 2.cos \: x. \frac{ \sqrt{3} }{2}$

$= \sqrt{3} .cos \: x$