# Pythagorian Identities

Let “OPQ” be a triangle where angle POQ is , and it’s base be “x” and perpendicular “y” as shown in the picture below:

Then,

Appealing to the Pythagorian theorem, we have:

Now let us suppose op be “r” then:

And as:

and

We have:

Thus:

This is called the fundamental Pythagorian identity of trigonometry.

From this we can also develop other identities as:

Dividing both side of fundamental Pythagorian identity by

Hence ,

And now dividing both side of fundamental Pythagorian identity by

Thus ,

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