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9. The German mathematician Karl Weierstrass (1815-1897) noticed that the substitution t tan(x/2) will convert any rational function of sin x and cos x into an ordinary rational function of t. %3D

9. The German mathematician Karl Weierstrass (1815-1897) noticed that the substitution t tan(x/2) will convert any rational function of sin x and cos x into an ordinary rational function of t. %3D

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 51E
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Question
59. The German mathematician Karl Weierstrass (1815-1897) noticed that the substitution t= tan(x/2) will convert any rational function of sin x and cos x into an ordinary rational function of t. (a) If t= tan(x/2 < X< 1, Sketeha right wiangle or use trigonemetric identities to show that %3D an V1 + t (b) Show that 2t cos x and sin x 1 + ? (c) Show that dx dt
Transcribed Image Text:59. The German mathematician Karl Weierstrass (1815-1897) noticed that the substitution t= tan(x/2) will convert any rational function of sin x and cos x into an ordinary rational function of t. (a) If t= tan(x/2 < X< 1, Sketeha right wiangle or use trigonemetric identities to show that %3D an V1 + t (b) Show that 2t cos x and sin x 1 + ? (c) Show that dx dt
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