write the value of cos squared theta minus one upon sin squared theta
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AN IDENTITY IS AN EQUALITY that is true for any value of the variable. (An equation is an equality that is true only for certain values of the variable.)
In algebra, for example, we have this identity:
(x + 5)(x − 5) = x2 − 25.
The significance of an identity is that, in calculation, we may replace either member with the other. We use an identity to give an expression a more convenient form. In calculus and all its applications, the trigonometric identities are of central importance.
On this page we will present the main identities. The student will have no better way of practicing algebra than by proving them. Links to the proofs are below.
Reciprocal identities
sin θ = 1
csc θ csc θ = 1
sin θ cos θ = 1
sec θ sec θ = 1
cos θ tan θ = 1
cot θ cot θ = 1
tan θ
In algebra, for example, we have this identity:
(x + 5)(x − 5) = x2 − 25.
The significance of an identity is that, in calculation, we may replace either member with the other. We use an identity to give an expression a more convenient form. In calculus and all its applications, the trigonometric identities are of central importance.
On this page we will present the main identities. The student will have no better way of practicing algebra than by proving them. Links to the proofs are below.
Reciprocal identities
sin θ = 1
csc θ csc θ = 1
sin θ cos θ = 1
sec θ sec θ = 1
cos θ tan θ = 1
cot θ cot θ = 1
tan θ
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