Trigonometric Identities

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24 Terms

1
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1 (Pythagorean Identity)

= sin²θ + cos²θ

2
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1 (Pythagorean Identity)

= sec²θ - tan²θ

3
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1 (Pythagorean Identity)

= csc²θ - cot²θ

4
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sin (2θ) =

2sinθ cosθ

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cos (2θ) =

cos²θ - sin²θ

2cos²θ - 1

1 - 2sin²θ

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tan (2θ) =

(2tanθ) / (1 - tan²θ)

7
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sin A + sin B =

2 sin[(A+B)/ 2] cos[(A-B)/ 2]

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sin A - sin B =

2 cos[(A+B)/ 2] sin [(A-B)/ 2]

9
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cos A + cos B =

2 cos[(A+B)/ 2] cos[(A-B)/ 2]

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cos A - cos B =

-2 sin[(A+B)/ 2] sin[(A-B)/ 2]

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sin(A+B) =

sinA cosB + cosA sinB

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sin (A-B) =

sinA cosB - cosA sinB

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cos(A+B) =

cosA cos B - sinA sinB

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cos(A-B) =

cosA cos B + sinA sinB

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tan(A+B) =

(tanA + tan B) / (1 - tanA tanB)

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tan(A-B) =

(tanA - tan B) / (1 + tanA tanB)

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sin²θ =

[1 - cos(2θ)] / 2

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cos²θ =

[1 + cos(2θ)] / 2

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tan²θ =

[1 - cos(2θ)] / [1 + cos(2θ)]

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sinA sinB =

½ [cos(A-B) - cos(A+B)]

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cosA cosB =

½ [cos(A-B) + cos(A+B)]

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sinA cosB =

½ [sin(A+B) + sin(A-B)]

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cosA sinB =

½ [(sin(A+B) - sin(A-B)]

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the only even trig identity

cos(-θ) = cos(θ)