Question

sin x + cos(x+30°) =0

Answer 1

the values of x are 120 degrees and -60 degrees

Answer 2

Thus, the value of $x$  is $120$°

Step-by-step explanation:

Given;

$sinx+cos(x+30)=0$

∴ $sinx+cos(x+30)=0$

⇒$sinx+cosxcos30-sinxsin30=0$

⇒$sinx+\frac{\sqrt{3} cosx}{2} -\frac{sinx}{2} =0$ (∵$cos30=\frac{\sqrt{3} }{2}$ and $sin30=\frac{1}{2}$)

⇒$\frac{\sqrt{3} cosx}{2} +\frac{sinx}{2} =0$

⇒$cosxcos30+sinxsin30=0$

⇒$cos(x-30)=0$  or  $cos(30-x)=0$

∴$cos(x-30)=0$

⇒$cos(x-30)=cos90$

⇒$x-30=90$

∴$x=120$°

And,

∴$cos(30-x)=0$

⇒$cos(30-x)=cos90$

⇒$30-x=90$

⇒$x=30-90$

∴$x=-60$°

Because negative angle is not possible.

∴ The value of $x$  is $120$°