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cos + cos 30 + cos 50+ sin+sin 30+ sin 50+ ..... + cos(2n-1)0 = ......+ sin(2n-1)0 : = sin 2n 2 sin 0 sin² no sin 0

cos + cos 30 + cos 50+ sin+sin 30+ sin 50+ ..... + cos(2n-1)0 = ......+ sin(2n-1)0 : = sin 2n 2 sin 0 sin² no sin 0

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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8. Prove that (a) (b) d de cos + cos 30 + cos 50 + (b) sin + sin 30 + sin 50+ Hint: Use Euler's formula and Geometric progression. 9. Prove that (a) 1 + cos 0 + cos 20 + sin+sin 20 + 10. Using the following definitions: sin (a) sin²+ cos² 0 = 1 (b) (cos) = sin 0 (c,d) sin(0₁ ±0₂) = sin 0₁ cos 0₂ (e,f) cos(0₁±0₂) = cos 0₁ cos 0₂ = ρύθ 2i + cos(2n-1)0 = - cos 0₁ sin 0₂ sin 0₁ sin 02 + sin(2n − 1)0 = + sin(n − 1)0: + cos(n − 1)0 = -i0 and cos sin - COS (n-1)0 2 sin sin 2n0 2 sin 0 sin² no sin 0 -1)0 no sin 2 2 sin sin 2 no 2 et+e-, show that 2
Transcribed Image Text:8. Prove that (a) (b) d de cos + cos 30 + cos 50 + (b) sin + sin 30 + sin 50+ Hint: Use Euler's formula and Geometric progression. 9. Prove that (a) 1 + cos 0 + cos 20 + sin+sin 20 + 10. Using the following definitions: sin (a) sin²+ cos² 0 = 1 (b) (cos) = sin 0 (c,d) sin(0₁ ±0₂) = sin 0₁ cos 0₂ (e,f) cos(0₁±0₂) = cos 0₁ cos 0₂ = ρύθ 2i + cos(2n-1)0 = - cos 0₁ sin 0₂ sin 0₁ sin 02 + sin(2n − 1)0 = + sin(n − 1)0: + cos(n − 1)0 = -i0 and cos sin - COS (n-1)0 2 sin sin 2n0 2 sin 0 sin² no sin 0 -1)0 no sin 2 2 sin sin 2 no 2 et+e-, show that 2
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