How do we show that cos2x

     

Cite this page as follows:

"Why 2sinxsin3x-cos2x=cos4x? I tried with this 2sinx*sin3x=2*1/2(cos2x-cos4x)=cos2x-cos4x..." dongan-group.com.vn Editorial, 25 Dec. 2011, https://www.dongan-group.com.vn/homework-help/why-2sinxsin3x-cos2x-cos4x-264605.Accessed 30 Dec. 2022.

Bạn đang xem: How do we show that cos2x


Who are the experts?Our certified Educators are real professors, teachers, and scholars who use their academic expertise to tackle your toughest questions. Educators go through a rigorous application process, và every answer they submit is reviewed by our in-house editorial team.



Use the formula for the triple of the argument:

`sin 3x = 3sin x - 4 sin^3 x`

Use the formula for the double of the argument:

`cos 2x = 1 - 2 sin^2 x`

Write the left side of the equation:

`2sin x*(3sin x - 4 sin^3 x) - 1 + 2 sin^2 x = cos 4x` 

`6sin^2 x - 8sin^4 x - 1 + 2 sin^2 x = cos 4x`

`8sin^2 x - 8sin^4 x - 1 = cos 2*(2x)`

`8sin^2 x - 8sin^4 x - 1 = 1 - 2sin^2 (2x)`

`8sin^2 x - 8sin^4 x -2 = - 2sin (2x)*sin(2x)`

`8sin^2 x - 8sin^4 x -2 = -8 sin^2 x*cos^2 x`

Using the basic formula of trigonometry yields:

`8sin^2 x - 8sin^4 x -2 = -8 sin^2 x*(1 - sin^2 x)`

`8sin^2 x - 8sin^4 x -2 = -8 sin^2 x+ 8sin^4 x`

This last line proves that `2sin x*sin 3x-cos 2x != cos 4x` .


Approved by dongan-group.com.vn Editorial Team

beckden
Educator since 2011

561 answers


| Certified Educator
cốt truyện Link

cốt truyện Page Citation Cite
I think you wrote the problem down wrong.

cos(2x) - 2 sin(x)sin(3x) = cos(4x)

First use the cos addition và subtraction formulas

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

cos(a-b) = cos(a)cos(b) + sin(a)sin(b)

Subtract cos(a-b) from cos(a+b) and the cos(a)cos(b) term disappears.

Xem thêm: Suy Nghĩ Về Quê Hương, Đất Nước (Dàn Ý, Cảm Nghĩ Của Em Về Quê Hương Năm 2021 (Dàn Ý

cos(a+b) - cos(a-b) = -2sin(a)sin(b)

For our problem mix a = 3x, b = x

cos(3x + x) - cos(3x - x) = -2sin(3x)sin(x)

cos(4x) - cos(2x) = -2 sin(x) sin(3x)

cos(4x) = cos(2x) - 2 sin(x) sin(3x)

If you use pi/4 you get

cos(4pi/4) = cos(2pi/4) - 2 sin(pi/4) sin(3pi/4)

cos(pi) = -1, cos(pi/2) = 0, sin(pi/4) = sqrt(2)/2 and sin(3pi/4) = sqrt(2)/2

so -1 = 0 - 2(sqrt(2)/2)(sqrt(2)/2)

-1 = - 2(2/4)

-1 = -1 checks....

Does not work with your formula....


Approved by dongan-group.com.vn Editorial Team

Ask a tutor

Ask a tutor
Assignment Type
Choose a reason Homework assignment Exam preparation Essay/thesis outline
Hover for more information.
Let us know your assignment type and we"ll make sure to lớn get you exactly the kind of answer you need.


Submit Question
Try out our Essay Lab!

With our Essay Lab, you can create a customized outline within seconds khổng lồ get started on your essay right away.

Xem thêm: Phong Trào Cải Cách Tôn Giáo ? Vì Sao Xuất Hiện Phong Trào Cải Cách Tôn Giáo

Start an Essay
icon-close


Start Your Essay

*
Start an Essay

Related Questions


See all

Popular Questions

Browse All
Math

Latest answer posted September 07, 2010 at 12:47:25 PM


What vì the letters R, Q, N, và Z mean in math?


14 Educator answers

Math

Latest answer posted October 07, 2013 at 8:13:27 PM


How do I determine if this equation is a linear function or a nonlinear function?


84 Educator answers

Math

Latest answer posted November 14, 2011 at 5:49:28 AM


Solve for b2:A= 1/2h (b1+b2) 


1 Educator answer

Math

Latest answer posted October 03, 2011 at 2:12:01 PM


This limit represents the derivative of some function f at some number a. State this f & a. Lim h->0 <(4th root of)(16+h)-2>/h a=? f=?


1 Educator answer

Math

Latest answer posted August 17, 2010 at 8:49:11 AM


Given f(x) and g(x), please find (fog)(X) và (gof)(x)f(x) = 2x g(x) = x+3


8 Educator answers
dongan-group.com.vn will help you with any book or any question. Our summaries & analyses are written by experts, and your questions are answered by real teachers.

Join dongan-group.com.vn


Apply to be an Educator

Recommended

More


©2022 dongan-group.com.vn, Inc. All Rights Reserved