LCHL Maths – Trigonometry 4 – Identities and proofs

Leaving Cert Higher Level Maths LCHL Maths – Trigonometry 4 – Identities and proofs

LCHL Trigonometry 4 — Identities and Proofs

Your progress through this topic0 of 13 lessons

Lessons in this topic

All 13 lessons, in order — each one ticks off as you open it.

1Miscellaneous 2Compound angle formula 3Double angle formula 4Products to sums and differences/ Sums and differences to products 5Quadratic equations 6Trig Proof 1 7Trig proof 2 8Trig Proof 3 9Trig Proof 4 10Trig proof 5 11Trig proof 6 12Trig Proof 7 13Trig Proof 8

The eight trigonometric proofs (Paper 2)

Trig Proof 1 — cos²A + sin²A = 1 (Pythagorean identity)Trig Proof 2 — the Sine Rule: a/sin A = b/sin B = c/sin CTrig Proof 3 — the Cosine Rule: a² = b² + c² − 2bc·cos ATrig Proof 4 — cos(A−B) = cos A cos B + sin A sin BTrig Proof 5 — cos(A+B) = cos A cos B − sin A sin BTrig Proof 6 — cos 2A = cos²A − sin²ATrig Proof 7 — sin(A+B) = sin A cos B + cos A sin BTrig Proof 8 — tan(A+B) = (tan A + tan B)/(1 − tan A tan B)

Key ideas in this topic

Compound angle (sin) — Compound angle (sin)Trigonometry 4.1

Compound angle (cos) — Compound angle (cos)Trigonometry 4.1

Compound angle (tan) — Compound angle (tan)Trigonometry 4.1

Double angle (sin) — Double angle (sin)Trigonometry 4.2

Double angle (cos) — Double angle (cos)Trigonometry 4.2

Double angle (tan) — Double angle (tan)Trigonometry 4.2

Sums to products & products to sums (page 15 of the log tables)

cos A + cos B — cos A + cos BTrigonometry 4.3

cos A − cos B — note the leading minus — cos A − cos B — note the leading minusTrigonometry 4.3

sin A + sin B — sin A + sin BTrigonometry 4.3

sin A − sin B — cos and sin swap — sin A − sin B — cos and sin swapTrigonometry 4.3

2 cos A cos B — 2 cos A cos BTrigonometry 4.3

2 sin A sin B — minus on the right — 2 sin A sin B — minus on the rightTrigonometry 4.3

2 sin A cos B — 2 sin A cos BTrigonometry 4.3

2 cos A sin B — 2 cos A sin BTrigonometry 4.3

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2023 Paper 2 Q2 →2023 Paper 2 Q4 →2021 Paper 2 Q4 →2016 Paper 2 Q3 →2015 Paper 1 Q9 →

Topic Content

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Trigonometry 4.0 – Miscellaneous

Trigonometry 4.1: Compound angle formula

Trigonometry 4.2: Double angle formula

Trigonometry 4.3: Products to sums and differences/ Sums and differences to products

Trigonometry 4.4: Quadratic equations

Trigonometry 4.5 – Trig Proof 1

Trigonometry 4.6 – Trig proof 2

Trigonometry 4.7 – Trig Proof 3

Trigonometry 4.8 – Trig Proof 4

Trigonometry 4.9 – Trig proof 5

Trigonometry 4.10 – Trig proof 6

Trigonometry 4.11 – Trig Proof 7

Trigonometry 4.12 – Trig Proof 8