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

Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter5: Identities And Formulas
Section5.4: Half-angle Formulas
Problem 69PS
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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
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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