Trigonometric Equations Question 206
Question: In $ \Delta ABC, $ if $ \cot A,\cot B,\cot C $ be in A. P., then $ a^{2},b^{2},c^{2} $ are in
[MP PET 1997]
Options:
A) H. P.
B) G. P.
C) A. P.
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- $ \cot A,\cot B $ and $ \cot C $ are in A. P.
Þ $ \cot A+\cot C=2\cot B $
Þ $ \frac{\cos A}{\sin A}+\frac{\cos C}{\sin C}=\frac{2\cos B}{\sin B} $
Þ $ \frac{b^{2}+c^{2}-a^{2}}{2bc(ka)}+\frac{a^{2}+b^{2}-c^{2}}{2ab(kc)}=2\frac{a^{2}+c^{2}-b^{2}}{2ac(kb)} $
Þ $ a^{2}+c^{2}=2b^{2} $ . Hence $ a^{2},b^{2},c^{2} $ are in A. P. Note : Students should remember this question as a fact.
BETA
