find the exact value of cos 15 degrees.
To find the exact value of cos 15 degrees, we can use the trigonometric identity known as "cosine of a sum":
cos (A + B) = cos A * cos B - sin A * sin B
In this case, let's rewrite 15 degrees as the sum of two angles: 15 degrees = 45 degrees - 30 degrees.
Now, we know the exact values of cosine and sine for 45 degrees and 30 degrees:
cos 45 degrees = √2/2
sin 45 degrees = √2/2
cos 30 degrees = √3/2
sin 30 degrees = 1/2
Using the cosine of a sum identity, we can calculate cos 15 degrees as follows:
cos 15 degrees = cos (45 degrees - 30 degrees)
= cos 45 degrees * cos 30 degrees + sin 45 degrees * sin 30 degrees
= (√2/2) * (√3/2) + (√2/2) * (1/2)
= √6/4 + √2/4
= (√6 + √2)/4
Therefore, the exact value of cos 15 degrees is (√6 + √2)/4.