Sum and differences identities equations

In summary, the equivalent expression for cos(pi/2 + x) - cos(pi/2 - x) is -2sin(x). This can be found by using the sum and difference formulas for cosine, with a=pi/2 and b=x, separately for each term. The first term results in 0 and the second term results in -2sin(x), giving us the final answer of -2sin(x).
  • #1
keishaap
13
0

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!
 
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  • #2
keishaap said:

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.
 
  • #3
Dick said:
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
 
  • #4
keishaap said:
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)?
 
  • #5
Cos (pi/2) =0
Sin(pi/2)= 1
 
  • #6
keishaap said:
Cos (pi/2) =0
Sin(pi/2)= 1

Ok, do go on. So what is cos(pi/2-x)?
 
  • #7
How come the b is not a -x ?
 
  • #8
So cos( 0-x)?
 
  • #9
keishaap said:
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.
 
  • #10
keishaap said:
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.
 
  • #11
Dick said:
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
 
  • #12
keishaap said:
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.
 
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  • #13
Dick said:
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!
 

1. What are sum and difference identities equations?

Sum and difference identities equations are mathematical equations that express the relationship between the sum or difference of two angles or trigonometric functions. These equations are used to simplify trigonometric expressions and solve problems involving multiple angles.

2. How do you prove sum and difference identities equations?

Sum and difference identities equations can be proved using the fundamental trigonometric identities, such as the Pythagorean identities and the double angle identities. These identities can be used to manipulate the equations and show that both sides are equal.

3. What are some examples of sum and difference identities equations?

Examples of sum and difference identities equations include: sin(A + B) = sinAcosB + cosAsinB, cos(A - B) = cosAcosB + sinAsinB, and tan(A + B) = (tanA + tanB) / (1 - tanAtanB). These equations can be used to find the value of trigonometric functions for multiple angles.

4. How are sum and difference identities equations used in real-life applications?

Sum and difference identities equations are used in various fields such as engineering, physics, and navigation. They are used to calculate the angles and distances between objects, as well as to analyze and predict the behavior of waves, sound, and light.

5. How can I remember sum and difference identities equations?

A helpful way to remember sum and difference identities equations is by using the acronym "SOHCAHTOA", which stands for sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent. This can serve as a guide to help you recall and apply the equations when needed.

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