Trigonometric Equations Question 319
Question: In any triangle ABC, the value of $ a(b^{2}+c^{2})\cos A+b(c^{2}+a^{2})\cos B+c(a^{2}+b^{2})\cos C $ is
[MP PET 1994]
Options:
A) $ 3abc^{2} $
B) $ 3a^{2}bc $
C) $ 3abc $
D) $ 3ab^{2}c $
Show Answer
Answer:
Correct Answer: C
Solution:
- $ ab^{2}\cos A+ba^{2}\cos B+ac^{2}\cos A+ca^{2}\cos C $ $ +bc^{2}\cos B+b^{2}c\cos C $ $ =ab(b\cos A+a\cos B)+acc,(\cos A+a\cos C) $ $ +bc(c\cos B+b\cos C) $ = $ abc+abc+abc=3abc $ .
BETA
