Write the expression as a function of $x$ , with no angle measure involved
$\cos (\frac{π}{6} + x)$
$\cos (\frac{π}{6} + x) =$
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Answer

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Answer

$\cos (\frac{π}{6} + x) = \frac{\sqrt{3}}{2} \cos (x) - \frac{1}{2} \sin (x)$

Steps

Step 1 ：Given the expression $\cos (\frac{π}{6} + x)$

Step 2 ：We can simplify this using the cosine sum identity, which states that $\cos (a + b) = \cos (a) \cos (b) - \sin (a) \sin (b)$ . In this case, $a = \frac{π}{6}$ and $b = x$ .

Step 3 ：Substituting $a$ and $b$ into the cosine sum identity, we get $\cos (\frac{π}{6} + x) = \cos (\frac{π}{6}) \cos (x) - \sin (\frac{π}{6}) \sin (x)$

Step 4 ：Since $\cos (\frac{π}{6}) = \frac{\sqrt{3}}{2}$ and $\sin (\frac{π}{6}) = \frac{1}{2}$ , we can substitute these values into the equation to get $\cos (\frac{π}{6} + x) = \frac{\sqrt{3}}{2} \cos (x) - \frac{1}{2} \sin (x)$

Step 5 ： $\cos (\frac{π}{6} + x) = \frac{\sqrt{3}}{2} \cos (x) - \frac{1}{2} \sin (x)$

Write the expression as a function of x, with no angle measure involvedcos⁡(π6+x)cos⁡(π6+x)=(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Answer

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Write the expression as a function of $x$ , with no angle measure involved
$\cos (\frac{π}{6} + x)$
$\cos (\frac{π}{6} + x) =$
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)