Given information: tan x sin x-cos x sin x+sin x cos x cos x-2cos'x Formula Used:

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 44E
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Hello, bartleby solves the attached equation by making the left look like the right.  I was trying to do it the other way and make the right look like the left and got stuck.  Could someone please show me how to make the right side look like the left?

Given information:
tan x
sinx+sin x cos x
sin x-cos x
cos x-2cos'x
Formula Used:
Pythagorean Identity Algebraic Identity
Ratio Identity
sin'x = 1- cos'x
|(a + b) (a – b) = a² - b tan x =
cos x
sin x
Calculation:
Steps
Description
Given Identity. To prove this
identity, we transform the left
side into the right side.
tan x
sin*x+sinx cos X
sin x-cosx
cos x-2cos'x
Multiplying the conjugate of
the sin x- cos x in top and
bottom
tan x
tan x-(sin x+cos x)
sin x-cos x
(sin x-cos x)-(sin x+cos x)
Applying the Algebraic
identity
|(a+b) (a – b) = a – b?
tan x-(sin x+cos x)
sin'x-cos?x
(sin x+cos x) Applying the Pythagorean
1-2cos?x
tan x-(sin x+cos x)
= tan x.
I-cos?x-cos?x
Identity in the denominator
sin x
(sin x+cos x)
Applying the Ratio Identity
(1-2cos?x)
CoS X
Multiply numerator with
sin fsin r+cos r)
Transcribed Image Text:Given information: tan x sinx+sin x cos x sin x-cos x cos x-2cos'x Formula Used: Pythagorean Identity Algebraic Identity Ratio Identity sin'x = 1- cos'x |(a + b) (a – b) = a² - b tan x = cos x sin x Calculation: Steps Description Given Identity. To prove this identity, we transform the left side into the right side. tan x sin*x+sinx cos X sin x-cosx cos x-2cos'x Multiplying the conjugate of the sin x- cos x in top and bottom tan x tan x-(sin x+cos x) sin x-cos x (sin x-cos x)-(sin x+cos x) Applying the Algebraic identity |(a+b) (a – b) = a – b? tan x-(sin x+cos x) sin'x-cos?x (sin x+cos x) Applying the Pythagorean 1-2cos?x tan x-(sin x+cos x) = tan x. I-cos?x-cos?x Identity in the denominator sin x (sin x+cos x) Applying the Ratio Identity (1-2cos?x) CoS X Multiply numerator with sin fsin r+cos r)
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Swokowski
Publisher:
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