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Unformatted text preview: Section 6.1 Trigonometric Identities Definition. An equation is an identity if the equation holds for values of the variables for which both sides of the quation are defined. Example. ( x + 1) 2 = x 2 + 2 x + 1 is an identity. Example. sec x = 1 cos x is an identity. Definition. An equation that is not an identity is called a conditional equation . Example. ( x + 1) 2 = x 2 + 1 is a conditional equation. Example. cos x = x + 1 is a conditional equation. Important Identities sin 2 + cos 2 = 1 1 + tan 2 = sec 2 1 + cot 2 = csc 2 Proving Identities One must be careful about the mathematical operations he/she uses, when trying to prove an equation is an identity, because one must eventually show that the equation holds for all defined values of the variable in order to prove the equation is an identity. You can use know identities when proving identities You need to find only one value of the variable for which the equation does not hold in order to show that the equation is not an identity...
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