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ALMultiple Choice

Sum and Difference Identities

Question 1 • IC Pre-Cal - Deering

How would you apply the Cosine Angle Difference Identity to find the exact value of cos 75o?

Answer
A
cos (100.5o – 25.5o)
B
cos (120o – 45o)
C
cos (180o – 75o)
D
cos (30o + 45o)

Explanation

Write 75° as 120° − 45°, so choice B lets you use the cosine difference identity: cos(a − b) = cos a cos b + sin a sin b. Substituting gives cos 75° = (−1/2)(√2/2) + (√3/2)(√2/2) = (√6 − √2)/4. These angles have familiar exact trigonometric values, making this a useful way to find the exact value.

AI-written and checked against the verified answer.

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