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 1 + cos t sin t %3D 1+ cos t sin t(1 - cos t) 1 - sin t(1 - cos t) 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.
sin t
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
en Shot
1...7.59 PM
denominator, and reduce.
1
Cos t
sin t
sin t
%D
1 + cos t
1 + cos t
sin t(1
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..8.07 PM
cos t)
%D
1
sin t(1 – cos t)
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1..8.27 PM
·Cos t
sin t
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Transcribed Image Text:Prove that the following identity is true. sin t 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 en Shot 1...7.59 PM denominator, and reduce. 1 Cos t sin t sin t %D 1 + cos t 1 + cos t sin t(1 en Shot ..8.07 PM cos t) %D 1 sin t(1 – cos t) en Shot 1..8.27 PM ·Cos t sin t Need Help? Read It en Shot
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