Manipal Entrance Test 2014 Math Paper

Given, cos2A+cos2C=sin2B
Obviously it is not an equilateral triangle because A=B=C=60° does not satisfy the given condition. But B=90°, then sin2B=1 and
cos2A+cos2C=cos2A+cos2(

π

2

−A )
=cos2A+sin2A=1
Hence, this satisfies the condition, so it is a right angled triangle but not necessarily isosceles triangle.