Find the sum $$M= \cos(2x)+\cos(4x)+\cos(6x)+\cos(8x)+\ldots+\cos(2016x)$$
2026-03-29 03:36:44.1774755404
How to find the sum $\cos(2x)+\cos(4x)+\cos(6x)+\cos(8x)+\ldots+\cos(2016x)$?
1.9k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in TRIGONOMETRY
- Is there a trigonometric identity that implies the Riemann Hypothesis?
- Finding the value of cot 142.5°
- Using trigonometric identities to simply the following expression $\tan\frac{\pi}{5} + 2\tan\frac{2\pi}{5}+ 4\cot\frac{4\pi}{5}=\cot\frac{\pi}{5}$
- Derive the conditions $xy<1$ for $\tan^{-1}x+\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy}$ and $xy>-1$ for $\tan^{-1}x-\tan^{-1}y=\tan^{-1}\frac{x-y}{1+xy}$
- Sine of the sum of two solutions of $a\cos\theta + b \sin\theta = c$
- Tan of difference of two angles given as sum of sines and cosines
- Limit of $\sqrt x \sin(1/x)$ where $x$ approaches positive infinity
- $\int \ x\sqrt{1-x^2}\,dx$, by the substitution $x= \cos t$
- Why are extraneous solutions created here?
- I cannot solve this simple looking trigonometric question
Related Questions in TRIGONOMETRIC-SERIES
- Can you please tell me if such an identity exists
- Finding value of $\sin(2^\circ)\cdot \sin(4^\circ)\cdot\cdot \cdot \sin(88^\circ)$
- The asymptotic behaviour of a sequence involving the sine and cosine functions: explain an strategy to get it
- Sum of the series $\csc^{-1} \sqrt{10}+ \csc^{-1} \sqrt{50}+\csc^{-1}\sqrt{170}...$
- partial sum of the series involving trigonometric function
- What is the advantage of using maclaurin expansion of functions like tan(x) over using the functions themselves?
- Prove the sum equation
- A conjecture about the asymptotic of the absolute value of $\sum_{k=1}^n\sin\left(N_k\right)$, where $N_k$ is the primorial of order $k$
- Sum of a trigonometric series involving sin and tan
- A very challenging question integral of an infinite product.
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Invoke the geometric series theorem on this.
$$\sum_{k=1}^{1008} \cos(2kx) = \Re\left(\sum_{k=1}^{1008} e^{2ikx}\right).$$