Question

If $\cos ^ { 2 } A + \cos ^ { 2 } C = \sin ^ { 2 } B$ then $\triangle A B C$ is .

• A. Equilateral
• B. Right angled
• C. Isosceles
• D. None of these

Answer 1

Answer: (B)

Right angled

Answer 2

It is obvious.

Trick : Obviously it is not an equilateral triangle because A = B = C = 60^o does not satisfy the given condition. But B = 90^o then $\sin ^ { 2 } B = 1$ and

$\cos ^ { 2 } A + \cos ^ { 2 } C = \cos ^ { 2 } A + \cos ^ { 2 } \left( \frac { \pi } { 2 } - A \right)$

$= \cos ^ { 2 } A + \sin ^ { 2 } A = 1$

Hence this satisfy the condition, so it is a right angle triangle but not necessarily isosceles.