Trigonometric Equations Question 214
Question: If $ {{\cos }^{2}}A+{{\cos }^{2}}C={{\sin }^{2}}B, $ then $ \Delta ABC $ is
[MP PET 1991]
Options:
A) Equilateral
B) Right angled
C) Isosceles
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- It is obvious. Trick: Obviously it is not an equilateral triangle because A=B=C=60o does not satisfy the given condition. But B = 90o then $ {{\sin }^{2}}B=1 $ and $ {{\cos }^{2}}A+{{\cos }^{2}}C={{\cos }^{2}}A+{{\cos }^{2}}( \frac{\pi }{2}-A ), $ $ =,{{\cos }^{2}}A+{{\sin }^{2}}A=1 $ Hence this satisfy the condition, so it is a right angle triangle but not necessarily isosceles.
BETA
