Examples using Pythagorean identities

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.

I have divided the questions up into sections that use the highlighted identities which you should learn.

Pythagorean Identities:

  •     \[{{{\sin }^2}\theta  + {{\cos }^2}\theta  \equiv 1}\]

  •     \[{1 + {{\tan }^2}\theta  \equiv {{\sec }^2}\theta }\]

  •     \[{1 + {{\cot }^2}\theta  \equiv {\rm{cose}}{{\rm{c}}^2}\theta }\]

Prove:

  1. \dfrac{\sin A}{1 + \cos A} + \dfrac{1 + \cos A}{\sin A} \equiv \dfrac{2}{\sin A}

Prove:

  1. \dfrac{1 - {{\cos }^2}x}{\cos x + 1} \equiv 1 - \cos x

Prove:

  1. \dfrac{\cos A}{\sin A} + \tan A \equiv \dfrac{1}{\sin A \cos A}

Prove:

  1. {\sec ^2}\theta  + {\cot ^2}\theta  \equiv {\tan ^2}\theta  + {\rm{ cose}}{{\rm{c}}^2}\theta

Prove:

  1. \dfrac{{1 - \cos \theta }}{{\sin \theta }} \equiv \dfrac{1}{{\mathrm{cosec } \theta}  + \cot \theta }

Prove:

  1. \dfrac{\cos \theta }{1 - \sin \theta }+\dfrac{1 - \sin \theta }{\cos \theta } \equiv 2\sec \theta

Prove:

  1.     \[{\rm{co}}{{\rm{s}}^{\rm{4}}}\theta  - {\sin ^4}\theta  + 1 \equiv 2{\cos ^2}\theta \]

Prove:

  1. \dfrac{\mathrm{cosec } \theta }{\cot \theta  + \tan \theta } \equiv \cos \theta




2018-08-08T15:23:24+00:00
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