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4. Prove that for all real x and y we have S(x+y) = S(x)C(y)+C(x)S(y) and that C(x+y) = C(x)C(y) - S(x)S(y).

4. Prove that for all real x and y we have S(x+y) = S(x)C(y)+C(x)S(y) and that C(x+y) = C(x)C(y) - S(x)S(y).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. Prove that for all real x and y we have S(x+y) = S(x)C(y)+C(x)S(y) and that C(x+y) = C(x)C(y) = S(x)S(y).
Transcribed Image Text:4. Prove that for all real x and y we have S(x+y) = S(x)C(y)+C(x)S(y) and that C(x+y) = C(x)C(y) = S(x)S(y).
For example suppose we want to try to calculate the area of the set S = {(x, y) : x ≤ 1,0 ≤ y ≤ f(x)}, Exercise 4.5. (On Cantor "middle" third set). Recall the construction of the Cantor set which is defined as C = Fk, where: Fo= [0, 1], F₁ = [0,1/3] U [2/3, 1] = [0, 1] \ (1/3,2/3),
Transcribed Image Text:For example suppose we want to try to calculate the area of the set S = {(x, y) : x ≤ 1,0 ≤ y ≤ f(x)}, Exercise 4.5. (On Cantor "middle" third set). Recall the construction of the Cantor set which is defined as C = Fk, where: Fo= [0, 1], F₁ = [0,1/3] U [2/3, 1] = [0, 1] \ (1/3,2/3),
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