Question

In \( \triangle ABC \), if \( \cos^2 A + \cos^2 B + \cos^2 C = 1 \), then \( \triangle ABC \) is:

• A. An equilateral triangle
• B. An isosceles triangle
• C. A right-angled triangle
• D. A scalene triangle

Hint:

In problems involving trigonometric identities for the angles of a triangle, check for well-known relationships such as the Pythagorean identity for right-angled triangles.

Answer 1

The Correct Option is C

We are given the equation \( \cos^2 A + \cos^2 B + \cos^2 C = 1 \) for the angles \( A \), \( B \), and \( C \) of \( \triangle ABC \). Step 1: This identity holds true when \( \triangle ABC \) is a right-angled triangle, as it satisfies the Pythagorean identity for the angles. Thus, the correct answer is a right-angled triangle.