What is the value of cos(15degrees)? a. root6 - root2/2
b. root6 - root2/4
c. root6 + root2/4
d. root6 + root2/2

The answer is root 6 + root 2/4

Step-by-step explanation:

Cos (15)

Rewrite the expression

write (15 degrees) as a difference

cos ( 45 degrees - 30 degrees)

cos ( 45 degrees - 30 degrees)

Expand the expression

Use cos ( t - s ) = cos (t) cos (s) + sin (t) sin (s)

to expand the expression

cos (45 degrees) cos ( 30 degrees) + sin ( 45 degrees ) sin ( 30 degrees)

cos (45 degrees) cos ( 30 degrees) + sin ( 45 degrees ) sin ( 30 degrees)

calculate the expression

use the trigonometric values table or unit circle to calculate the expression

root 2/root 2 × cos (30 degrees) + sin (45 degrees) sin (30 degrees)

root 2/root 2 × root 3/root 2 + sin (45 degrees) sin (30 degrees)

root 2/ root 2 × root 3/root 2 + root 2/root 2 × sin (30 degrees)

root 2/root2 × root 3/root 2 + root 2/root 2 × 1/2

root 2/root2 × root 3/root 2 + root 2/root 2 × 1/2

Multiply

root 2/root 2 × root 3/root 2 only

Multiply by the fractions

root 6/ root 4 + root 2/ root 2 × 1/2

Multiply root 2/ root 2 × 1/2 only

6 root / root 4 + root 2/ root 4

write all numerators above the denominator

root 6 + root 2 / 4