UPSC 2015 CDS I Math Paper

Remember:
If a triangle is inscribed in a circle such that the sum of the squares of sides of the triangle is equal to twice the square of diameter, then the triangle is a right-angled triangle whose hypotenuse is the same as the diameter of the circle.In right ΔABC,
∴sin2A+sin2B+sin2C
=sin290∘+sin2B+sin2(90∘−B)
=1+sin2B+cos2B
=2‌‌‌‌(sin2θ+cos2θ=1)