Q.1 (ii) In triangle ABC , (a + b)·cos C + (b + c)cos A + (c + a)·cos B is equal to _____. A. a - b + c B. a + b - c C. a + b + c D. a - b - c

In \(\triangle ABC\), \((a + b)\cdot\cos C + (b + c)\cos A + (c + a)\cdot\cos B\) is equal to _____.

Q.1 (ii) In \(\triangle ABC\), \((a + b)\cdot\cos C + (b + c)\cos A + (c + a)\cdot\cos B\) is equal to _____.

A. \(a - b + c\)

B. \(a + b - c\)

C. \(a + b + c\)

D. \(a - b - c\)

Doubtly Asked 28 Oct 2026 Board exam · March 2025 hsc 12th Save WhatsApp Report

Best answer

Answer: C. \(a + b + c\)

Answer: (c) \(a + b + c\)

Regroup the terms and use the projection rule:

\((b\cos C + c\cos B) + (c\cos A + a\cos C) + (a\cos B + b\cos A) = a + b + c\),

since \(a = b\cos C + c\cos B\), \(b = c\cos A + a\cos C\) and \(c = a\cos B + b\cos A\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

Was this answer helpful?