t-Formulae ~ 01 ~ Three Ways to Derive Them

One of my subscribers asked me to explain what t-formulae are, and how they are used in trigonometry. This is the first of three videos that I created in response to that request (thank you, Kristyn).

I firmly believe that it is a good idea to practise deriving significant formulae and identities as part of your regular study. In this way, you become intimately acquainted with each 'formula' and can also see how it is connected with the foundational concepts for that topic/area of study. You also learn basic methods for manipulating the symbols algebraically.

Therefore, this first video is devoted to demonstrating three different ways in which you could derive the t-Formulae. If you wish to skip to each method of derivation here are the key sections of the video:
02:05 ~ Explanation of what t-Formulae ARE
03:55 ~ Derivation #01 ~ Using Double-Angle Formulae
12:40 ~ Derivation #02 ~ Using a 'Half-Angle' Triangle
18:10 ~ Derivation #03 ~ Using a 'Full'-Angled Triangle

I suggest that you adopt the method that you like most and practise using it until you can derive the t-Formulae with ease!

In the second video I will demonstrate how t-formulae can be used to solve certain kinds of trigonometric equations.

In the third video I will explain how the t-formulae can help you evaluate particular kinds of integrals.

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