To find the value of cos 15°, we can use the cosine addition identity: cos(a ± b) = cos a cos b ∓ sin a sin b.
We can express 15° as the difference of two angles that we know the cosine and sine for: 15° = 45° – 30°.
Now, we can set a = 45° and b = 30°:
cos(15°) = cos(45° – 30°)
Using the cosine identity, we get:
cos(15°) = cos 45° cos 30° + sin 45° sin 30°
Now we need the values of cos 45°, cos 30°, sin 45°, and sin 30°:
- cos 45° = √2/2
- cos 30° = √3/2
- sin 45° = √2/2
- sin 30° = 1/2
Substituting these values back into our equation:
cos(15°) = (√2/2)(√3/2) + (√2/2)(1/2)
This can be simplified:
cos(15°) = (√6/4) + (√2/4)
Now combine the terms:
cos(15°) = (√6 + √2) / 4
So, the value of cos 15° is (√6 + √2) / 4.