sin(A – B) COs A cos B = tan A – tan B We begin on the left side of the equation by using a Difference Formula on the numerator. We can then separate the expression into two fractions and reduce. Lastly, we use a Ratio Identity to simplify. sin A cos B – cos A · sin(A – B) cos A cos B %3D cos A cos B sin A cos B cos A cos B cos A • COs A cos B sin A cos A COS B = tan A – tan B

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 60E
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Prove the identity.
sin(A – B)
= tan A
tan B
COs A cos B
We begin on the left side of the equation by using a Difference Formula on the numerator. We can then separate the
expression into two fractions and reduce. Lastly, we use a Ratio Identity to simplify.
sin(A – B)
COs A cos B
sin A cos B
Cos A
COs A cos B
sin A cos B
COs A ·
COs A cos B
COs A cos B
sin A
%D
COs A
Cos B
= tan A
tan B
Transcribed Image Text:Prove the identity. sin(A – B) = tan A tan B COs A cos B We begin on the left side of the equation by using a Difference Formula on the numerator. We can then separate the expression into two fractions and reduce. Lastly, we use a Ratio Identity to simplify. sin(A – B) COs A cos B sin A cos B Cos A COs A cos B sin A cos B COs A · COs A cos B COs A cos B sin A %D COs A Cos B = tan A tan B
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