Trigonometric Equations Question 187
Question: If the angles of a triangle $ ABC $ be in A.P., then
Options:
A) $ c^{2}=a^{2}+b^{2}-ab $
B) $ b^{2}=a^{2}+c^{2}-ac $
C) $ a^{2}=b^{2}+c^{2}-ac $
D) $ b^{2}=a^{2}+c^{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
- A, B, C are in A. P. then angle $ B=60^{o}, $ $ \cos B=\frac{a^{2}+c^{2}-b^{2}}{2ac} $ , $ { \begin{aligned} & \text{since }A+B+C=180^{o}and \\ & \text{ }A+C=2B\Rightarrow B=60^{o} \\ \end{aligned} } $
Þ $ \frac{1}{2}=\frac{a^{2}+c^{2}-b^{2}}{2ac}\Rightarrow a^{2}+c^{2}-b^{2}=ac $
Þ $ b^{2}=a^{2}+c^{2}-ac $ .
BETA
