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Basic Trigonometric Identities

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Reciprocal Identity for Cotangent

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tan(θ)=1cot(θ)\tan(\theta) = \frac{1}{\cot(\theta)}

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Quotient Identity for Cotangent

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cot(θ)=cos(θ)sin(θ)\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}

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Reciprocal Identity for Cosecant

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sin(θ)=1csc(θ)\sin(\theta) = \frac{1}{\csc(\theta)}

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Pythagorean Identity for Tangent and Secant

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tan2(θ)+1=sec2(θ)\tan^2(\theta) + 1 = \sec^2(\theta)

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Quotient Identity for Tangent

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tan(θ)=sin(θ)cos(θ)\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}

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Pythagorean Identity

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sin2(θ)+cos2(θ)=1\sin^2(\theta) + \cos^2(\theta) = 1

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Reciprocal Identity for Sine

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csc(θ)=1sin(θ)\csc(\theta) = \frac{1}{\sin(\theta)}

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Reciprocal Identity for Secant

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cos(θ)=1sec(θ)\cos(\theta) = \frac{1}{\sec(\theta)}

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Reciprocal Identity for Tangent

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cot(θ)=1tan(θ)\cot(\theta) = \frac{1}{\tan(\theta)}

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Reciprocal Identity for Cosine

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sec(θ)=1cos(θ)\sec(\theta) = \frac{1}{\cos(\theta)}

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