I suggest that it is (sin A)^2 + (cos A)^2 = 1
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An identity is like an equation which is true for all values of the variable.
plane trigonometry spherical trigonometry
The main kinds are plane trigonometry and solid trigonometry. The latter will include trigonometry in hyper-spaces.
Hipparchus is the father of trigonometry.
Trigonometry based on a unit circle and radians and trigonometry based on a right triangle.