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: $si{n}^2(x)+co{s}^2(x)=1.$

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