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5
questions
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How to get $A$ and $B$ from $A\csc 10^\circ+B=$ $\sin 10^\circ+\cos 60^\circ+\cos 40^\circ+\sin 70^\circ+\sin 90^\circ$?
The problem is as follows:
Find $A+B$ from:
$A\csc 10^\circ+B=\sin 10^\circ+\cos 60^\circ+\cos 40^\circ+\sin 70^\circ+\sin 90^\circ$
The alternatives given in my book are as follows:
$\begin{array}{ll}...
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1
vote
2
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How can we sum up $\sin^m$ and $\cos^m$ series when the angles are in arithmetic progression?
How can we sum up $\sin^m$ and $\cos^m$ series when the angles are in arithmetic progression?
Does an identity exist similar to 1.1 and 1.2 for $m>1$?, and
Does an approximate or estimate exist?
...
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1
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Using Euler and polynomials
I want to show that $\sum_{k=-N}^{N}e^{ikx}=\frac{\sin((N+\frac{1}{2})x)}{\sin(\frac{x}{2})}$ for $N\in \mathbb{N}$
Any tips on how to proceed?
I tried doing it in two ways:
First using the sum of ...
- 1,394
18
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1
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$\sum \cos$ when angles are in arithmetic progression [duplicate]
Possible Duplicate:
How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?
Prove $$\cos(\alpha) + \cos(\alpha + \beta) + \cos(\alpha + 2\beta) + \dots + \cos[\...
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195
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8
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101k
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How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?
How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression? For example here is the sum of $\cos$ series:
$$\sum_{k=0}^{n-1}\cos (a+k \cdot d) =\frac{\sin(n \times \frac{...
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