What is the Value of cos(15°)?

The exact value of cos(15°) in fraction/surd form is: cos(15°) = (√6 + √2) / 4

(In decimal form, it is approximately 0.9659).

To find this value, we express 15° as the difference between two standard angles that we already know: 45° and 30°. (Since 45 - 30 = 15).

Step 1: The Formula Use the cosine subtraction formula: cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

Step 2: Substitute the angles Let A = 45° and B = 30°. cos(45° - 30°) = cos(45°)cos(30°) + sin(45°)sin(30°)

Step 3: Insert standard table values We know that:

• cos(45°) = 1/√2
• cos(30°) = √3/2
• sin(45°) = 1/√2
• sin(30°) = 1/2

Step 4: Calculate cos(15°) = (1/√2) × (√3/2) + (1/√2) × (1/2) cos(15°) = (√3 / 2√2) + (1 / 2√2)

Since the denominators are the same, combine the numerators: cos(15°) = (√3 + 1) / 2√2

While the answer above is correct, mathematicians prefer not to leave square roots in the denominator. We multiply the top and bottom by √2:

= [ (√3 + 1) × √2 ] / [ 2√2 × √2 ] = (√6 + √2) / 4