What is the value of cos 15°?

• 1/2(√2 − √3)
• 1/2(√2 + √3)
• √2 + √3
• √2 − √3

The value of cos 15° can be calculated using the cosine subtraction formula. Specifically, cos 15° can be expressed as cos(45° - 30°).

Using the Cosine Formula

The cosine subtraction formula is:

cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

Applying the Values

• Let A = 45° and B = 30°.
• cos(45°) = √2/2
• cos(30°) = √3/2
• sin(45°) = √2/2
• sin(30°) = 1/2

Calculating cos 15°

Now, substituting these values into the formula:

cos(15°) = cos(45°)cos(30°) + sin(45°)sin(30°

cos(15°) = (√2/2)(√3/2) + (√2/2)(1/2)

cos(15°) = (√6/4) + (√2/4) = (√6 + √2)/4

Final Answer

Thus, the value of cos 15° is (√6 + √2)/4. This does not match any of the given options directly, but it can be approximated or simplified further if needed.