Proving identities using the addition formulae

You will be expected to be able to prove a trig. identity such as the examples below. In the videos I show you how to set out an identity and what to look for.

This is a tricky topic and one that I find students give in too quickly. Learn your formulae and have patience.

Addition Formulae (Compound Angles):

  • \sin (A + B) \equiv \sin A\cos B + \cos A\sin B
  • \sin (A - B) \equiv \sin A\cos B - \cos A\sin B
  • \cos (A + B) \equiv \cos A\cos B - \sin A\sin B
  • \cos (A - B) \equiv \cos A\cos B + \sin A\sin B
  • \tan (A + B) \equiv \dfrac{{\tan A + \tan B}}{{1 - \tan A\tan B}}
  • \tan (A - B) \equiv \dfrac{{\tan A - \tan B}}{{1 + \tan A\tan B}}

Prove:

  1. \dfrac{\sin (A + B)}{\sin (A - B)} \equiv \dfrac{\tan A + \tan B}{\tan A - \tan B}

Prove:

  1. \cot (A + B) \equiv \dfrac{\cot A\cot B - 1}{\cot A + \cot B}




2018-08-08T17:44:48+00:00
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