Question

This Question: 5 pts 1 of 26 (14 complete) In the following problem, the expression is the right side of the formula for cos(a - b) with particular values for a and B. cos solūcos(-a) + sin(72) sin(- a. Identify a and B in the expression. The value of a is The value of B is b. Write the expression as the cosine of an angle. The expression is cos c. Find the exact value of the expression. cos 12 cos - + sin 12 sin 12 (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Rationalize all denominators. Simplify your answer.)

Answer 1

a)

$cos\left (\frac{\pi }{12} \right )cos\left (\frac{-\pi }{12} \right )+sin\left (\frac{\pi }{12} \right )sin\left (\frac{-\pi }{12} \right )$

$Cos\left ( \alpha -\beta \right )=cos\alpha cos\beta +sin\alpha sin\beta$
The value of $\alpha =\frac{\pi }{12}$

The value of $\beta =\frac{-\pi }{12}$

b)

The expression cosine of anangle

$cos\left ( \frac{\pi }{12}- \left ( -\frac{\pi }{2} \right )\right )$

$=cos\left ( \frac{\pi }{12}+\frac{\pi }{12}\right )$

$=cos\left ( \frac{2\pi }{12}\right )$

$=cos\left ( \frac{\pi }{6}\right )$

c)

$cos\left (\frac{\pi }{12} \right )cos\left (\frac{-\pi }{12} \right )+sin\left (\frac{\pi }{12} \right )sin\left (\frac{-\pi }{12} \right )$$=cos\left ( \frac{\pi }{6}\right )$

                                                                                     $=\frac{\sqrt{3}}{2}$

e