Answer:
Step-by-step explanation:
I'm assuming you're trying to solve this for x. We use the difference identity for cosine and rewrite:
[tex]cos(x-30)=cosxcos30+sinxsin30[/tex] and simplify using the unit circle to help.
[tex]cosx(\frac{\sqrt{3} }{2})+sinx(\frac{1}{2})=0\\cosx(\frac{\sqrt{3} }{2})=-\frac{1}{2} sinx\\cosx=-\frac{1}{2}(\frac{2}{\sqrt{3} })sinx\\cosx=-\frac{1}{\sqrt{3} }sinx\\1=-\frac{1}{\sqrt{3} }\frac{sinx}{cosx}\\1=-\frac{1}{\sqrt{3} }tanx\\-\sqrt{3} =tanx[/tex]
and on the unit circle, the angle where the tangent is negative square root of 3 is -60° which is also a positive 300°
