Trigonometric Equations Question 157
Question: In a triangle $ ABC $ if $ 2a^{2}b^{2}+2b^{2}c^{2}= $ $ a^{4}+b^{4}+c^{4} $ , then angle B is equal to
Options:
A) $ 45^{o} $ or $ 135^{o} $
B) $ 135^{o} $ or $ 120^{o} $
C) $ 30^{o} $ or $ 60^{o} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- $ 2a^{2}b^{2}+2b^{2}c^{2}=a^{4}+b^{4}+c^{4} $ Also, $ {{(a^{2}-b^{2}+c^{2})}^{2}}= $ $ a^{4}+b^{4}+c^{4}-2(a^{2}b^{2}+b^{2}c^{2}-c^{2}a^{2}) $
Þ $ {{(a^{2}-b^{2}+c^{2})}^{2}}=2c^{2}a^{2} $ Þ $ \frac{a^{2}-b^{2}+c^{2}}{2ca}=\pm \frac{1}{\sqrt{2}}=\cos B $
Þ $ B=45^{o} $ or $ 135^{o} $ .
BETA
