Prove that the following identity is true. sin t 1+ cos t -1- cos t sin t We begin on the left side of the equation by multiplying the numerator and denominator by the conjugate of the denominator. We can then use a Pythagorean Identity on the denominator, an reduce. 1- cos t sin t 1 + cos t sin t 1 + cos t %3D sin t(1 - cos t) 1 - sin t(1 - cos t) %3D 1- cos t sin t
Prove that the following identity is true. sin t 1+ cos t -1- cos t sin t We begin on the left side of the equation by multiplying the numerator and denominator by the conjugate of the denominator. We can then use a Pythagorean Identity on the denominator, an reduce. 1- cos t sin t 1 + cos t sin t 1 + cos t %3D sin t(1 - cos t) 1 - sin t(1 - cos t) %3D 1- cos t sin t
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 68E
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Question
![Prove that the following identity is true.
1 - cos t
sin t
sin t
1 + cos t
We begin on the left side of the equation by multiplying the numerator and denominator by the conjugate of the denominator. We can then use a Pythagorean Identity on the denominator, and
reduce.
1
- cos t
sin t
sin t
%D
1 + cos t
1 + cos t
sin t(1 – cos t)
1
sin t(1 – cos t)
1
Cos t
sin t](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F576abf7e-c3b8-4513-8fc9-4c35b542b0f0%2F8733dd3a-9da9-4865-952d-54d1dc3f9821%2Fcy4oqjs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Prove that the following identity is true.
1 - cos t
sin t
sin t
1 + cos t
We begin on the left side of the equation by multiplying the numerator and denominator by the conjugate of the denominator. We can then use a Pythagorean Identity on the denominator, and
reduce.
1
- cos t
sin t
sin t
%D
1 + cos t
1 + cos t
sin t(1 – cos t)
1
sin t(1 – cos t)
1
Cos t
sin t
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