I am working though my maths courses

[morbello]

using double angle formula and intergration.

i was wanting to know why the the squared eitherside of the equals sign stayed the same.i thought square one side of the equals sign is root the otherside.

this is some of my working.


cos(2x)=2cos^2_x-1
=cos^2_x-1=sin^2_x
2 cos ^2_x-1= sin^2_x sin^2_x
cos(2X)=Sin^2_x sin^2_x
2√sinx=cos(2x)
how does
2√sinx=cos^2_x


2√cosx=1/2 sin (2X)+c
the answer is
cos^2_x =1/4 sin (2x)+1/2x+c

The Attempt at a Solution

 

[SteamKing]

i was wanting to know why the the squared eitherside of the equals sign stayed the same.i thought square one side of the equals sign is root the otherside.

Why would you think that?

2^2 = 2*2 = 4

x^2 = x*x

 

[Mark44]

using double angle formula and intergration.

i was wanting to know why the the squared eitherside of the equals sign stayed the same.i thought square one side of the equals sign is root the otherside.

this is some of my working.


cos(2x)=2cos^2_x-1
=cos^2_x-1=sin^2_x

? What are you doing here?
Also, don't connect equations with =. One equation is not "equal" to another.
The line just above is wrong - it should be 1 - cos2/SUP](x) = sin2/SUP](x), but even so, how is it related to the line just above it?

2 cos ^2_x-1= sin^2_x sin^2_x

?

cos(2X)=Sin^2_x sin^2_x
2√sinx=cos(2x)
how does
2√sinx=cos^2_x


2√cosx=1/2 sin (2X)+c
the answer is
cos^2_x =1/4 sin (2x)+1/2x+c

The Attempt at a Solution

 

[TimeToShine]

Anything you do to an equation you must do to both sides.

If you square one side then you must square the other.

As for your workings there is an error in the second line.

 

[morbello]

you have said that everything you do to one side of the equals sign, you do to the other.what if you only want the a and not the a^2.what would you do to the equation.could you also tell me if you move -1 to the LHS of the equation will it be +1.Is there laws for the LHS and the RHS of equations.Like foils law or bodmass.

 

[CAF123]

you have said that everything you do to one side of the equals sign, you do to the other.what if you only want the a and not the a^2.what would you do to the equation

Do you mean if you have $a^2 = ...$, then how to get $a = ...$? Consider this: If x = 7, say, then x² = 49. How would you undo this operation?

Like foils law or bodmass.

I wouldn't really call them laws, just mnemonics so as to remember how to multiply out binomials and order of operations when dealing with numbers.

 

[HallsofIvy]

you have said that everything you do to one side of the equals sign, you do to the other.what if you only want the a and not the a^2.

To go from a^2 to a, you obviously have to take the square root. So if you have a^2 on one side of the equation (and NO other "a" in th equation) you take the square root of both sides of the equation.

what would you do to the equation.could you also tell me if you move -1 to the LHS of the equation will it be +1.Is there laws for the LHS and the RHS of equations.Like foils law or bodmass.

You don't "move -1 to the LHS". If you want to get ride of "-1" on one side of the equation you add 1 to both sides of the equation. -1+ 1= 0 so that will get rid of the -1.

You talk as if these were totally arbitrary rules. The idea that -1+ 1= 0 is a basic fact of arithmetic. And the idea that if a= b then f(a)= f(b), for any function f, is a basic logical statement.

 

[morbello]

If like the -1 you add 1 to both sides.would it be the same as or some thing like. x^2 and add ^-2 to both sides.

 

[HallsofIvy]

I have no idea what you could mean by "add ^-2". "^-2" is not a number (in fact, by itself if does not mean anything) and so cannot be "added". Do you understand what x^2 and x^-2 mean?