write the expression as a function of x, with no angle measure involved. \n\ncos (\\frac{5\\pi}{6}+x)\n\ncos…

write the expression as a function of x, with no angle measure involved. \n\ncos (\\frac{5\\pi}{6}+x)\n\ncos (\\frac{5\\pi}{6}+x)=\\square \n(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

write the expression as a function of x, with no angle measure involved. \n\ncos (\\frac{5\\pi}{6}+x)\n\ncos (\\frac{5\\pi}{6}+x)=\\square \n(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Use the cosine addition formula

The cosine addition formula is $\cos(A + B)=\cos A\cos B-\sin A\sin B$. Here $A=\frac{5\pi}{6}$ and $B = x$. So, $\cos(\frac{5\pi}{6}+x)=\cos\frac{5\pi}{6}\cos x-\sin\frac{5\pi}{6}\sin x$.

Step2: Find the values of $\cos\frac{5\pi}{6}$ and $\sin\frac{5\pi}{6}$

We know that $\cos\frac{5\pi}{6}=-\frac{\sqrt{3}}{2}$ and $\sin\frac{5\pi}{6}=\frac{1}{2}$. Substitute these values into the expression: $\cos(\frac{5\pi}{6}+x)=-\frac{\sqrt{3}}{2}\cos x-\frac{1}{2}\sin x$.

Answer:

$-\frac{\sqrt{3}}{2}\cos x-\frac{1}{2}\sin x$