Answer:
cos(x-30)=1/2
Step-by-step explanation:
We use the following relationship to obtain cos(x)
[tex]sin^{2}(x) +cos^{2}(x) +1[/tex]
From that, we have that cos(x)= sqrt(1-1/4)=sqrt(3) / 4
To obtain the value of cos(x-30), lets remember the following expression:
[tex]cos(a-b)=cos(a)*cos(b)+sin(a)*sin(b)[/tex]
Therefor, we can use that to obtain our desired function cos(x-30)
cos(x)*cos(30)+sin(x)*sin(30)
[tex]\frac{\sqrt{3} }{2} * \frac{\sqrt{3} }{2} +\frac{-1}{2}*\frac{1}{2}[/tex]
=2/4=1/2
