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 the above

Answer 1

Answer: (B)

Given, $\cos ^{2} A+\cos ^{2} C=\sin ^{2} B$
Obviously it is not an equilateral triangle because $A=B=C=60^{\circ}$ does not satisfy the given condition.
But $B=90^{\circ}$, then $\sin ^{2} B=1$ and $\cos ^{2} A+\cos ^{2} C=\cos ^{2} A+\cos ^{2}\left(\frac{\pi}{2}-A\right)$
Hence, this satisfies the condition, so it is a right angled triangle but not necessarily isosceles triangle.