Sum and differences identities equations

[keishaap]

Homework Statement

Which is equivalent to: cos(∏/2 + x) - cos(∏/2 - x)?
A) -2cos(x)
B) -2
C) 0
D)-2sin(x)

Homework Equations

Cos (A-B)

The Attempt at a Solution

I am totally stuck :( please help!

 

[Dick]

Homework Statement

Which is equivalent to: cos(∏/2 + x) - cos(∏/2 - x)?
A) -2cos(x)
B) -2
C) 0
D)-2sin(x)

Homework Equations

Cos (A-B)

The Attempt at a Solution

I am totally stuck :( please help!

You mentioned the sum and difference formulas. I think you should try to use them.

 

[keishaap]

You mentioned the sum and difference formulas. I think you should try to use them.

I have tried to use them but i totally get stuck like i don't know which is a or b and we are only given cos (a-b) = cosAcosB + sinAsinB

 

[Dick]

I have tried to use them but i totally get stuck like i don't know which is a or b and we are only given cos (a-b) = cosAcosB + sinAsinB

In cos(pi/2-x) the 'a' is pi/2 and the 'b' is x. So what does that turn into? What are cos(pi/2) and sin(pi/2)?

 

[keishaap]

Cos (pi/2) =0
Sin(pi/2)= 1

 

[Dick]

Cos (pi/2) =0
Sin(pi/2)= 1

Ok, do go on. So what is cos(pi/2-x)?

 

[keishaap]

How come the b is not a -x ?

 

[keishaap]

So cos( 0-x)?

 

[SteamKing]

I have tried to use them but i totally get stuck like i don't know which is a or b and we are only given cos (a-b) = cosAcosB + sinAsinB

It doesn't matter. Pick one angle and make it A. The other then must be B.

 

[Dick]

How come the b is not a -x ?

Why would you think that?? If you have a formula for cos(a-b) and you want to apply it to cos(pi/2-x) then you should put a=pi/2 and b=x. Your formula already has the '-' in it. Just use the formula and stop trying to double think it.

 

[keishaap]

Why would you think that?? If you have a formula for cos(a-b) and you want to apply it to cos(pi/2-x) then you should put a=pi/2 and b=x. Your formula already has the '-' in it. Just use the formula and stop trying to double think it.

But the formula also has pi/2 + x there's 2 A's and 2 B's

 

[Dick]

But the formula also has pi/2 + x there's 2 A's and 2 B's

Use the formula SEPARATELY for each one. You can choose them differently for cos(pi/2-x) and cos(pi/2+x). Finish cos(pi/2-x) first, then worry about the other one.

 

[keishaap]

Use the formula SEPARATELY for each one. You can choose them differently for cos(pi/2-x) and cos(pi/2+x). Finish cos(pi/2-x) first, then worry about the other one.

Okay i thought they had to be the same because the teacher didn't show us any other way thanks!