Triangles And Properties Of Triangle Question 26
Question: In a $ \Delta ABC, $ $ \frac{\sin A}{\sin C}=\frac{\sin (A-B)}{\sin (B-C)}, $ then $ a^{2},b^{2},c^{2} $ are such that
Options:
A) $ b^{2}=ac $
B) $ b^{2}=\frac{a^{2}c^{2}}{a^{2}+c^{2}} $
C) They are in A.P.
D) $ b^{2}=a^{2}+c^{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ \frac{\sin A}{\sin C}=\frac{\sin (A-B)}{\sin (B-C)}\Rightarrow \frac{\sin (B+C)}{\sin (A+B)}=\frac{\sin (A-B)}{\sin (B-C)} $
$ \Rightarrow {{\sin }^{2}}B-{{\sin }^{2}}C={{\sin }^{2}}A-{{\sin }^{2}}B $
$ \Rightarrow {{\sin }^{2}}A,{{\sin }^{2}}B,{{\sin }^{2}}C $ and hence $ a^{2},b^{2},c^{2} $ are in A.P.
BETA
