Triangles And Properties Of Triangle Question 33
Question: If $ A+B+C=\pi , $ then $ \cos 2A+\cos 2B+\cos 2C+4\sin A\sin B\sin C $ is equal to:
Options:
A) 0
B) 1
C) 2
D) 3
Show Answer
Answer:
Correct Answer: B
Solution:
[b] If $ A+B+C=\pi , $ then $ \cos mA+\cos mB+\cos mC $ $ =1-4\sin \frac{mA}{2}\sin \frac{mB}{2}\sin \frac{mC}{2} $
$ \therefore $ For $ m=2:\cos 2A+\cos 2B+\cos 2C $ $ =1-4\sin A\sin B\sin C $
$ \Rightarrow \cos 2A+\cos 2B+\cos 2C $ $ +4\sin A\sin BsinC=1 $
BETA
