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The exact value of cos 5π/12 is:
A) 0.99
B) 0.26
C) √2(√3-1)/4
D) √2(√3+1)/4

User Franklynd
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1 Answer

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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.

User The Grand User
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