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Prove that the following identity is true. sin2 tan x 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 simplify by reducing the common factor. sin x(sin x + cos x) sin2 xsin x cos x Cos X 1 - cos X 2 cos3 x cos x) sin x(sin x = sin2 xcos2 x COS X sin x cos x sin x sin2 x - COS X sin x cos x = tan x sin2 x sin x cos x = tan x. (sin x - cos x) tan x sin x - cos x

Prove that the following identity is true. sin2 tan x 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 simplify by reducing the common factor. sin x(sin x + cos x) sin2 xsin x cos x Cos X 1 - cos X 2 cos3 x cos x) sin x(sin x = sin2 xcos2 x COS X sin x cos x sin x sin2 x - COS X sin x cos x = tan x sin2 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
Section: Chapter Questions
Problem 4T
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Prove that the following identity is true. sin2 tan x 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 simplify by reducing the common factor. sin x(sin x + cos x) sin2 xsin x cos x Cos X 1 - cos X 2 cos3 x cos x) sin x(sin x = sin2 xcos2 x COS X sin x cos x sin x sin2 x - COS X sin x cos x = tan x sin2 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. sin2 tan x 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 simplify by reducing the common factor. sin x(sin x + cos x) sin2 xsin x cos x Cos X 1 - cos X 2 cos3 x cos x) sin x(sin x = sin2 xcos2 x COS X sin x cos x sin x sin2 x - COS X sin x cos x = tan x sin2 x sin x cos x = tan x. (sin x - cos x) tan x sin x - cos x
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