Question

If A, B, C are the angles of a triangle, then sin² A + sin² B + sin² C – 2 cos A cos B cos C is equal to ______.

विकल्प

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Answer 1

If A, B, C are the angles of a triangle, then sin² A + sin² B + sin² C – 2 cos A cos B cos C is equal to 2.

Explanation:

sin² A + sin² B + sin² C

= 1 – cos² A + 1 – cos² B + sin² C

= 2 – cos² A – cos(B + C) cos(B – C)

= 2 – cos A[cos A – cos(B – C)]

= 2 – cos A[– cos(B + C) – cos(B – C)

= 2 + cos A . 2 cos B cos C

∴ sin² A + sin² B + sin² C – 2 cos A cos B cos C = 2