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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 72E
Related questions
Question
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e1fbffb-2297-4291-a738-2b18bf8495d6%2F6eb1958b-ae4d-4062-befa-0ccba278f060%2Fy8icnd_processed.png&w=3840&q=75)
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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