How do I evaluate?......?

Question

cos(A+B)=(cosA)(cosB)+(sinA)(sinB)
find 15 degrees.

Answer 1

First off, your identity is incorrect.

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

To find the cosine of 15 degrees, express 15 degrees as a difference.
15 = 45 - 30

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

Fortunately for us, we know the coordinates of 45 degrees and 30 degrees on the unit circle.

cos(45 - 30) = [sqrt(2)/2] [sqrt(3)/2] + [sqrt(2)/2] [1/2]

Simplifying,

= [sqrt(2)sqrt(3)]/4 + sqrt(2)/4

Merging them into one fraction

= [ sqrt(2) sqrt(3) + sqrt(2) ] / 4

Factor out sqrt(2) from the top,

cos(15) = sqrt(2) [sqrt(3) + 1] / 4

Rule of thumb: Always express your answer in its exact form. That may mean leaving radicals the way they are, as opposed to approximating radicals with a calculator. For instance, leave sqrt(2) as sqrt(2) and not 1.414. The exception is if they ask you on a test to calculate a value to 3 decimal places.

Answer 2

let A = 10 degrees and B= 5 degrees. Then plug tat into the formula.

Answer 3

Use 45 and -30 degrees, both of which have calculable trig functions.