A trigonometry identity, which is derived from Pythagorean Theorem is called Pythagorean identity.
There are three possibilities to form Pythagorean identities in terms of trigonometric functions in trigonometry. They are used as formulas in trigonometry. So, it is very important to remember them to study the trigonometry.
The sum of the squares of the sine and cosine functions at an angle is equal one.
$\sin^2{\theta} + \cos^2{\theta} = 1$
The subtraction of the square of tangent function from square of secant function at an angle is equal to one.
$\sec^2{\theta} \,-\, \tan^2{\theta} = 1$
The subtraction of the square of cotangent function from square of cosecant function at an angle is equal to one.
$\csc^2{\theta} \,-\, \cot^2{\theta} = 1$
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