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Questions and Answers
What is the formula for cos(A + B)?
The formula sin(π/2-A) = cos A is always true.
True
What is the formula for tan(A+B)?
[(tan A + tan B)/(1 – tan A tan B)]
The formula for sin(A -B) is _______.
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Match the following trigonometric identities with their formulas:
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What is the formula for cos3A?
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What is the value of sin(π-A) in terms of sin A?
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The formula tan(A+B) = [(tan A + tan B)/(1 + tan A tan B)] is always true.
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What is the formula for cos2A in terms of sin A and cos A?
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The formula sin(A+B) sin(A–B) = _______
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What is the value of tan 2A in terms of tan A?
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Match the following trigonometric identities with their formulas:
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The formula sin(A+B) = sin A cos B + cos A sin B is always true.
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Study Notes
Trigonometric Identities: Sum and Difference Formulas
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cos(A + B) = cos A cos B – sin A sin B -
cos(A – B) = cos A cos B + sin A sin B -
sin(A+B) = sin A cos B + cos A sin B -
sin(A -B) = sin A cos B – cos A sin B
Complementary Angle Identities
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sin(π/2-A) = cos A -
cos(π/2-A) = sin A -
sin(π-A) = sin A -
cos(π-A) = -cos A -
sin(π+A)=-sin A -
cos(π+A)=-cos A -
sin(2π-A) = -sin A -
cos(2π-A) = cos A
Tangent and Cotangent Identities
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tan(A+B) = [(tan A + tan B)/(1 – tan A tan B)](if none of the angles A, B, and (A ± B) is an odd multiple of π/2) -
tan(A-B) = [(tan A – tan B)/(1 + tan A tan B)](if none of the angles A, B, and (A ± B) is an odd multiple of π/2) -
cot(A+B) = [(cot A cot B − 1)/(cot B + cot A)](if none of the angles A, B, and (A ± B) is a multiple of π) -
cot(A-B) = [(cot A cot B + 1)/(cot B – cot A)](if none of the angles A, B, and (A ± B) is a multiple of π)
Product Identities
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cos(A+B) cos(A–B)=cos2A–sin2B=cos2B–sin2A -
sin(A+B) sin(A–B) = sin2A–sin2B=cos2B–cos2A
Sum-to-Product Identities
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sinA+sinB = 2 sin (A+B)/2 cos (A-B)/2
Double Angle Identities
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sin2A = 2sinA cosA = [2tan A /(1+tan2A)] -
cos2A = cos2A–sin2A = 1–2sin2A = 2cos2A–1= [(1-tan2A)/(1+tan2A)] -
tan 2A = (2 tan A)/(1-tan2A)
Triple Angle Identities
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sin3A = 3sinA – 4sin3A -
cos3A = 4cos3A – 3cosA -
tan3A = [3tanA–tan3A]/[1−3tan2A]
Trigonometric Identities: Sum and Difference Formulas
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cos(A + B) = cos A cos B – sin A sin B -
cos(A – B) = cos A cos B + sin A sin B -
sin(A+B) = sin A cos B + cos A sin B -
sin(A -B) = sin A cos B – cos A sin B
Complementary Angle Identities
-
sin(π/2-A) = cos A -
cos(π/2-A) = sin A -
sin(π-A) = sin A -
cos(π-A) = -cos A -
sin(π+A)=-sin A -
cos(π+A)=-cos A -
sin(2π-A) = -sin A -
cos(2π-A) = cos A
Tangent and Cotangent Identities
-
tan(A+B) = [(tan A + tan B)/(1 – tan A tan B)](if none of the angles A, B, and (A ± B) is an odd multiple of π/2) -
tan(A-B) = [(tan A – tan B)/(1 + tan A tan B)](if none of the angles A, B, and (A ± B) is an odd multiple of π/2) -
cot(A+B) = [(cot A cot B − 1)/(cot B + cot A)](if none of the angles A, B, and (A ± B) is a multiple of π) -
cot(A-B) = [(cot A cot B + 1)/(cot B – cot A)](if none of the angles A, B, and (A ± B) is a multiple of π)
Product Identities
-
cos(A+B) cos(A–B)=cos2A–sin2B=cos2B–sin2A -
sin(A+B) sin(A–B) = sin2A–sin2B=cos2B–cos2A
Sum-to-Product Identities
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sinA+sinB = 2 sin (A+B)/2 cos (A-B)/2
Double Angle Identities
-
sin2A = 2sinA cosA = [2tan A /(1+tan2A)] -
cos2A = cos2A–sin2A = 1–2sin2A = 2cos2A–1= [(1-tan2A)/(1+tan2A)] -
tan 2A = (2 tan A)/(1-tan2A)
Triple Angle Identities
-
sin3A = 3sinA – 4sin3A -
cos3A = 4cos3A – 3cosA -
tan3A = [3tanA–tan3A]/[1−3tan2A]
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Description
Formulas for trigonometric functions such as sin, cos, and tan with angle additions and subtractions. Includes identities for special angles like π/2 and π.
