Trigonometric Equations Question 107
Question: In $ \Delta ABC, $ if $ \sin A:\sin C=\sin (A-B):\sin (B-C), $ then
Options:
A) $ a,\ b,\ c $ are in A.P.
B) $ a^{2},\ b^{2},\ c^{2} $ are in A.P.
C) $ a^{2},\ b^{2},\ c^{2} $ are in G. P.
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- $ \frac{\sin A}{\sin C}=\frac{\sin (A-B)}{\sin (B-C)} $
$ \Rightarrow $ $ \sin (B+C)\sin (B-C)=\sin (A+B)\sin (A-B) $
$ \Rightarrow $ $ {{\sin }^{2}}B-{{\sin }^{2}}C={{\sin }^{2}}A-{{\sin }^{2}}B $
$ \Rightarrow $ $ 2{{\sin }^{2}}B={{\sin }^{2}}A+{{\sin }^{2}}C\Rightarrow 2b^{2}=a^{2}+c^{2} $ Hence $ a^{2},,b^{2},,c^{2} $ are in A.P.
BETA
