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Prove that the following identity is true. sin x tan x sin x cos x sin x - COs X cos x 2 cos x We begin on the right side of the equation by factoring the numerator and denominator. We can then use a Pythagorean Identity in the denominator and reduce. We can then use the ratio identity, and then factor the denominator. Finally we simp reducing the common factor. sin x(sin x + cos x) sin xsin x cos x coS x1 cos x 2 cos x sin x(sin x + cos x) sin xcos2 COS X sin x cos x sin x sin2 х — COS X cos x sin x = tan x sin x sin x cos x = tan x ' (sin x - cos x) tan x sin x - cos x

Prove that the following identity is true. sin x tan x sin x cos x sin x - COs X cos x 2 cos x We begin on the right side of the equation by factoring the numerator and denominator. We can then use a Pythagorean Identity in the denominator and reduce. We can then use the ratio identity, and then factor the denominator. Finally we simp reducing the common factor. sin x(sin x + cos x) sin xsin x cos x coS x1 cos x 2 cos x sin x(sin x + cos x) sin xcos2 COS X sin x cos x sin x sin2 х — COS X cos x sin x = tan x sin x sin x cos x = tan x ' (sin x - cos x) tan x sin x - cos x

Algebra & Trigonometry with Analytic Geometry
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 that the following identity is true. sin x tan x sin x cos x sin x - COs X cos x 2 cos x We begin on the right side of the equation by factoring the numerator and denominator. We can then use a Pythagorean Identity in the denominator and reduce. We can then use the ratio identity, and then factor the denominator. Finally we simp reducing the common factor. sin x(sin x + cos x) sin xsin x cos x coS x1 cos x 2 cos x sin x(sin x + cos x) sin xcos2 COS X sin x cos x sin x sin2 х — COS X cos x sin x = tan x sin x sin x cos x = tan x ' (sin x - cos x) tan x sin x - cos x
Transcribed Image Text:Prove that the following identity is true. sin x tan x sin x cos x sin x - COs X cos x 2 cos x We begin on the right side of the equation by factoring the numerator and denominator. We can then use a Pythagorean Identity in the denominator and reduce. We can then use the ratio identity, and then factor the denominator. Finally we simp reducing the common factor. sin x(sin x + cos x) sin xsin x cos x coS x1 cos x 2 cos x sin x(sin x + cos x) sin xcos2 COS X sin x cos x sin x sin2 х — COS X cos x sin x = tan x sin x sin x cos x = tan x ' (sin x - cos x) tan x sin x - cos x
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