Trigonometric-Identities Question 396
Question: If $ \frac{\sin A-\sin C}{\cos C-\cos A}=\cot B, $ then A,B,C are in
Options:
A) A.P.
B) G.P.
C) H.P.
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{\sin A-\sin C}{\cos C-\cos A}=\cot B $
Þ $ \frac{2\cos \frac{A+C}{2}\sin \frac{A-C}{2}}{2\sin \frac{A+C}{2}\sin \frac{A-C}{2}}=\cot B $
$ \Rightarrow \cot \frac{(A+C)}{2}=\cot B $
Þ $ B=\frac{A+C}{2} $ Thus A, B, C will be in A.P.
BETA
