Trig Formula

[vanbeersj]

I need to prove the given identity

cos(x-y) + sin(x+y) = (cosx + sinx)(cosy +sin y)

If I take the left side and expand it i get

cosxcosy + sinxsiny + sinxcosy + cosxsiny

I'm stumped at this point.......should I try the right side instead?

 

[mmm4444bot]

cos(x-y) + sin(x+y) = (cosx + sinx)(cosy +sin y)

If I take the left side and expand it i get

cosxcosy + sinxsiny + sinxcosy + cosxsiny This looks like the expansion of the righthand side.

Are you familiar with the addition and subtraction identities?

Apply them to cos(x - y) and sin(x + y).

Compare those results with your expansion of the righthand side.

 

[vanbeersj]

Im having difficulties with the addition and subtraction. I'm not sure where to start to expand the right hand side.

 

[mmm4444bot]

I'm not sure where to start to expand the right hand side.

Let's back up a step.

Do you know the difference between left and right?

Or, perhaps you're using the wrong terminology, when you say that you expanded the lefthand side.

Did you apply addition and subtraction identities to the lefthand side to obtain the expression you posted?

I can't tell what you're doing.

If you're actually trying to multiply together the two factors on the righthand side, then use FOIL.

 

[vanbeersj]

Do you know the difference between left and right?

Or, perhaps you're using the wrong terminology, when you say that you expanded the lefthand side.

Did you apply addition and subtraction identities to the lefthand side to obtain the expression you posted?

I can't tell what you're doing.

If you're actually trying to multiply together the two factors on the righthand side, then use FOIL.


I would hope I know my left from right.
On the leftside cos(x-y) +sin(x+y) the addition and subtraction identities and got cosxcosy + sinxsiny + sinxcosy + cosxsiny

If I focus on the right side of the equation (cosx+sinx) (cosy+siny)
then if I get cosxcosy+sinxsiny
which then I get cos(x-y) but I'm missing the sin(x+y) part of the equation to equal the left side

 

[mmm4444bot]

On the leftside cos(x-y) +sin(x+y) the addition and subtraction identities [gave] ... Okay, then. This is not what you originally said that you did.

Applying identities and expanding factors are not the same.

If I focus on the right side of the equation (cosx+sinx) (cosy+siny)

then if I get cosxcosy+sinxsiny This is wrong.

I told you to use FOIL, and you did not ask me what FOIL means, so I assume that you understand it.

You're not using FOIL properly.

Google FOIL, if you need to refresh your memory.

 

[vanbeersj]

I remeber FOIL, once I did it to the right side it makes the identity easier to see. Thanks for the help.

 

[Deleted member 4993]

I need to prove the given identity

cos(x-y) + sin(x+y) = (cosx + sinx)(cosy +sin y)

If I take the left side and expand it i get

cosxcosy + sinxsiny + sinxcosy + cosxsiny

= cos(x)*cos(y) + cos(x)*sin(y) + sin(x)*sin(y) + sin(x)*cos(y) .....................rearrenging above

= cos(x)*[cos(y) + sin(y)] + sin(x)* [sin(y) + cos(y)]

Now continue....
I'm stumped at this point.......should I try the right side instead?