Stitz-Zeager_College_Algebra_e-book

Rewrite the following as algebraic expressions of x

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Unformatted text preview: α + β ) sin(α) cos(β ) + cos(α) sin(β ) cos(α) cos(β ) − sin(α) sin(β ) sin( sin( Since tan(α) = cos(α) and tan(β ) = cos(β ) , it looks as though if we divide both numerator and α) β) denominator by cos(α) cos(β ) we will have what we want tan(α + β ) = 1 sin(α) cos(β ) + cos(α) sin(β ) cos(α) cos(β ) · 1 cos(α) cos(β ) − sin(α) sin(β ) cos(α) cos(β ) = cos(α) sin(β ) sin(α) cos(β ) + cos(α) cos(β ) cos(α) cos(β ) sin(α) sin(β ) cos(α) cos(β ) − cos(α) cos(β ) cos(α) cos(β ) = $ $ sin(α)$$β ) $$α) sin(β ) cos($ cos($ $ $ $ + cos(α) cos(β ) $ cos(α)$$β ) $$ cos( $ $ $ cos($ $α)$$β ) cos( sin(α) sin(β ) $ $cos(β ) − cos(α) cos(β ) $ $ $α)$$$ cos( $ = tan(α) + tan(β ) 1 − tan(α) tan(β ) Naturally, this formula is limited to those cases where all of the tangents are defined. The formula developed in Exercise 10.4.2 for tan(α + β ) can be used to find a formula for tan(α − β ) by rewriting the difference as a sum, tan(α +(−...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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