Let a, b be nonzero numbers. Prove that 2πT dt a² cos² (1) + b² sin² (1) by integrating on two homotopic (in C\{0}) curves: [0, 27], and 72 the unit circle. 2π ab' 71 (t) = a cos(t) + i b sin(t), tɛ
Let a, b be nonzero numbers. Prove that 2πT dt a² cos² (1) + b² sin² (1) by integrating on two homotopic (in C\{0}) curves: [0, 27], and 72 the unit circle. 2π ab' 71 (t) = a cos(t) + i b sin(t), tɛ
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.2: Trigonometric Equations
Problem 69E
Related questions
Question
![Let a, b be nonzero numbers. Prove that
•2π
dt
a² cos² (t) + b² sin² (t
=
2π
ab'
by integrating on two homotopic (in C\{0}) curves: 7₁ (t) = a cos(t) + i b sin(t), t =
[0, 27], and 72 the unit circle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe15ed467-90ec-4e60-afef-3d3f6119f74d%2Fe7e85eb7-6671-468a-8838-d5412ebd447f%2Ff3vzbgb_processed.png&w=3840&q=75)
Transcribed Image Text:Let a, b be nonzero numbers. Prove that
•2π
dt
a² cos² (t) + b² sin² (t
=
2π
ab'
by integrating on two homotopic (in C\{0}) curves: 7₁ (t) = a cos(t) + i b sin(t), t =
[0, 27], and 72 the unit circle.
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