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(mathematics, trigonometry) A trigonometric equation that is true for all values of the input variable for which both sides of the equation are defined.

Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same. For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them. The reciprocal identities arise as ratios of sides in the triangles where this unit line is no longer the hypotenuse. The triangle shaded blue illustrates the identity ${\displaystyle 1+\cot ^{2}\theta =\csc ^{2}\theta }$, and the red triangle shows that ${\displaystyle \tan ^{2}\theta +1=\sec ^{2}\theta }$.

(mathematics, trigonometry) A trigonometric equation that is true for all values of the input variable for which both sides of the equation are defined.

Transformation of coordinates (a,b) when shifting the reflection angle ${\displaystyle \alpha }$ in increments of ${\displaystyle {\frac {\pi }{4}}}$

(mathematics, trigonometry) A trigonometric equation that is true for all values of the input variable for which both sides of the equation are defined.

Transformation of coordinates (a,b) when shifting the angle ${\displaystyle \theta }$ in increments of ${\displaystyle {\frac {\pi }{2}}}$