Final answer:
The exact value of cos 5π/12 can be found using the cosine sum identity and standard trigonometric values, leading to the result √2(√3 - 1)/4. Option C
Step-by-step explanation:
The exact value of cos 5π/12 can be found using the cosine of a sum formula, since 5π/12 is not one of the standard angles for which we memorize the trigonometric values. We can express 5π/12 as π/4 + π/6. By using the cosine sum identity cos(a + b) = cos(a)cos(b) - sin(a)sin(b), we can find the exact value.
The cosine and sine values for π/4 and π/6 are √2/2, √3/2, and 1/2, respectively. Substituting these into the formula, we have:
cos(π/4 + π/6) = cos(π/4)cos(π/6) - sin(π/4)sin(π/6)
= (√2/2)(√3/2) - (√2/2)(1/2)
= √6/4 - √2/4
= (√6 - √2)/4
= √2(√3 - 1)/4
Thus, the exact value of cos 5π/12 is √2(√3 - 1)/4, which corresponds to the option C.