Trigonometry/Trigonometric identities

What is an identity?
An identity is an equation that holds true for all values of the variables appearing in it, because it either is a definition or is the logical consequence of a definition. An example of a definitional identity is $$\tan(x)=\frac{\sin(x)}{\cos(x)}.$$  An example of an identity that can logically be proven to hold for all values of its variable is the Pythagorean identity expressed in trigonometric form:  $$sin^2(x)+cos^2(x)=1.$$

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