The value of the trigonometric expression cos(75)cos(15) is 1/4 after applying the trigonometric identity.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have a trigonometric expression:
= cos(75°)cos(15°)
As we know the trigonometric identity:
cos(a)cos(b) = (1/2)[cos(a + b) + cos(a - b)]
a = 75
b = 15
Plug the above values in the trigonometric identity:
cos(75)cos(15) = (1/2)[cos(75 + 15) + cos(75 - 15)]
cos(75)cos(15) = (1/2)[cos(90) + cos(60)]
The trigonometric ratio is the ratio of the pair of a right-angled triangle.
The value of cos90 = 0
cos60 = 1/2
cos(75)cos(15) = (1/2)[0 + 1/2]
cos(75)cos(15) = 1/4
Thus, the value of the trigonometric expression cos(75)cos(15) is 1/4 after applying the trigonometric identity.
Learn more about trigonometry here:
brainly.com/question/26719838
#SPJ2
