Trigonometric Equations Question 134
Question: If in a triangle, $ a{{\cos }^{2}}\frac{C}{2}+c{{\cos }^{2}}\frac{A}{2}=\frac{3b}{2}, $ then its sides will be in
[MP PET 1982; AMU 2000; AIEEE 2003]
Options:
A) A. P.
B) G. P.
C) H. P.
D) A. G.
Show Answer
Answer:
Correct Answer: A
Solution:
- $ a\frac{s(s-c)}{ab}+c\frac{s(s-a)}{bc}=\frac{3b}{2} $
Þ $ 2s(s-c+s-a)=3b^{2} $
Þ $ 2s(b)=3b^{2}\Rightarrow 2s=3b $
Þ $ a+b+c=3b\Rightarrow a+c=2b\Rightarrow a,b,c $ are in A.P.
BETA
