write the expression as a function of x, with no angle measure involved. cos((5π/6)+x) cos((5π/6)+x)=□…

write the expression as a function of x, with no angle measure involved. cos((5π/6)+x) cos((5π/6)+x)=□ (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. cos((5π/6)+x) cos((5π/6)+x)=□ (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression)

Answer

Explanation:

Step1: Use cosine addition formula

$\cos(A + B)=\cos A\cos B-\sin A\sin B$, here $A = \frac{5\pi}{6}$ and $B=x$. $\cos\left(\frac{5\pi}{6}+x\right)=\cos\frac{5\pi}{6}\cos x-\sin\frac{5\pi}{6}\sin x$

Step2: Evaluate trig - function values

We know that $\cos\frac{5\pi}{6}=-\frac{\sqrt{3}}{2}$ and $\sin\frac{5\pi}{6}=\frac{1}{2}$. So $\cos\frac{5\pi}{6}\cos x-\sin\frac{5\pi}{6}\sin x=-\frac{\sqrt{3}}{2}\cos x-\frac{1}{2}\sin x$

Answer:

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