Question

Cosx-√3sinx=√3поділити почлено на 2​

Answer 1

$\displaystyle\bf\\Cosx-\sqrt{3} Sinx=\sqrt{3} \ |:2\\\\\\\frac{1}{2}Cosx-\frac{\sqrt{3} }{2}Sinx=\frac{\sqrt{3} }{2} \\\\\\Cos\frac{\pi }{3} Cosx-Sin\frac{\pi }{3}Sinx=\frac{\sqrt{3} }{2} \\\\\\Cos\Big(x+\frac{\pi }{3} \Big)=\frac{\sqrt{3} }{2} \\\\\\x+\frac{\pi }{3} =\pm arcCos\frac{\sqrt{3} }{2} +2\pi n,n\in Z\\\\\\x+\frac{\pi }{3} =\pm\frac{\pi }{6}+2\pi n,n\in Z\\\\\\x=\pm \frac{\pi }{6} -\frac{\pi }{3} +2\pi n,n\in Z$

Answer 2

To simplify the equation cos(x) - √3sin(x) = √3/2, we can divide both sides of the equation by 2.

(cos(x) - √3sin(x))/2 = (√3/2)/2

Simplifying the right side:

(cos(x) - √3sin(x))/2 = √3/4

So the simplified equation is (cos(x) - √3sin(x))/2 = √3/4.