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We can understand this identity in two different, useful ways.

Firstly, we can use Euler's identities from trigonometry to obtain the desired result using straightforward algebra. We know that:

Consider the triangle ABC. Denote h the altitude through B and D the point where h intersects the (extended) base AC
Cosine function for triangle ADB.

cos α= x/c  =>  x=c*cos α
 

Using: Tan(x) = Sin(x)/Cos(x)

Using: Cos(x) = sqrt(1-Sin²(x))

Cos(A) = sqrt(1-Sin²(A)) = sqrt(1-1/3) = sqrt(2)/sqrt(3)

Therefore: Tan(A) = Sin(A)/Cos(A) = (1/sqr...

The "chain rule" is a handy little tool that we can use to find the derivative of a complicated function.  Specifically, we use the chain rule when we have functions within functions.  But what ...

3. Quick maths.