Complete Proof of the Sine Rule & Cosine Rule (All Cases + 2 Methods Each)

In this video, we carry out a COMPLETE and EXHAUSTIVE proof of the Sine Rule and Cosine Rule, considering: Acute-angled triangles Obtuse-angled triangles Multiple proof methods Step-by-step explanations Geometric and trigonometric derivations This is one of the most detailed explanations you’ll find on the derivation of these important results in trigonometry. TIMESTAMPS SINE RULE Method 1 — Using Trigonometric Ratios (Height of Triangle) 00:00 — Acute-angled Triangle 10:37 — Obtuse-angled Triangle Method 2 — Using Circle Geometry 18:55 — Acute-angled Triangle 29:06 — Obtuse-angled Triangle COSINE RULE Method 1 — Using Trigonometric Ratios (Height of Triangle) 33:50 — Acute-angled Triangle 41:58 — Obtuse-angled Triangle Method 2 — Using Trigonometric Ratios and Algebra 48:24 — Full Derivation 1:00:33 — End Whether you're preparing for WAEC, NECO, JAMB, A-Level exams, or simply trying to deeply understand trigonometry, this lesson will help you see why these formulas work — not just how to use them.