Question

If in a \(\triangle ABC\), \(\sin^2 A + \sin^2 B + \sin^2 C = 2\), then the triangle is always:

• A. isosceles triangle
• B. right angled
• C. acute angled
• D. obtuse angled

Hint:

If product of cosines = 0 $\Rightarrow$ one angle is \(90^\circ\).

Answer 1

The Correct Option is B

Concept: \[ \sin^2 A + \sin^2 B + \sin^2 C = 2 + 2\cos A \cos B \cos C \]

Step 1: Given: \[ 2 = 2 + 2\cos A \cos B \cos C \] \[ \Rightarrow \cos A \cos B \cos C = 0 \]

Step 2: One angle must be \(90^\circ\) \[ \Rightarrow \text{triangle is right angled} \]