Trigonometric Identities Question 53
Question: If $ \alpha +\beta +\gamma =\pi $ then the minimum value of $ cosA+cosB+cosC $
Options:
A) is zero
B) is positive
C) lies between $ -2 $ and $ -3 $
D) is $ -3 $
Show Answer
Answer:
Correct Answer: D
Solution:
For all x, $ \cos x\ge -1 $
$ \therefore \cos A+\cos B+\cos C\ge -3 $ and equality holds if $ \cos A=\cos B=\cos C=-1, $ which can be attained if $ A=\pi ,B=\pi ,,C=-\pi $
BETA
