Consider the right-angled triangle below

Pythagoras' Theorem gives the equation

If we divide through by hyp² we get

This is the most common form of Pythagoras' theorem in trigonometry

This identity is used a lot in pure maths, and must be memorized.

If we divide by opp² or adj² we get alternative identities

and

In summary, the three forms of Pythagoras' Theorem in trigonometry are, in order of usefulness,

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