Examples using double angle 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 identities and have patience.

Double angle identities

  •     \begin{align*} \sin{2A} \equiv 2 \sin A \cos A \end{align} \\

        \begin{align*} \cos {2A} &\equiv \cos {^2{A}} - \sin {^2{A}} \\  &\equiv 2 \cos {^2{A}} - 1  \\  &\equiv 1 - 2 \sin {^2{A}} \end{align*} \\

        \begin{align*} \tan {2A} \equiv \dfrac{2 \tan A}{1 - \tan {^2{A}}} \end{align}


  1.     \[\dfrac{{1 - \cos 2A}}{{\sin 2A}} \equiv \tan A\]


  1. \tan \theta  + \cot \theta  \equiv 2{\rm{cosec}}2\theta


  1. \cos 4\theta  \equiv 8{\cos ^4}\theta  - 8{\cos ^2}\theta  + 1

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