What simpler indentity is equal to sin(x) - cos(x)

  • Thread starter Matt Jacques
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In summary, the conversation discusses trigonometric identities and how to solve for theta in a physics problem involving sin(x) - cos(x). It is mentioned that there isn't a simpler identity for this expression and references to websites for trig identities are provided. The conversation then shifts to a problem involving logarithms and the formula for loga(mn) is suggested. Finally, it is concluded that the solution for the logarithmic problem is ln100+3a-(5/2)c.
  • #1
Matt Jacques
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What simpler indentity is equal to sin(x) - cos(x) ?

Trig Identities have come back to haunt me!
 
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  • #2
Originally posted by Matt Jacques
What simpler indentity is equal to sin(x) - cos(x) ?

Trig Identities have come back to haunt me!

There isn't one. Plot out the two curves and look at their differences and you'll see it's not simpler than the basic sine curve.

There are lots of websites to check out trig identities if you need references. A quick google search will show more than you need, but most contain the same information. Here's three is you want to check them out:

http://www.math2.org/math/trig/identities.htm

http://aleph0.clarku.edu/~djoyce/java/trig/identities.html

http://www.mathwizz.com/algebra/help/help32.htm
 
  • #3
Then how do I solve for theta in a physics problem that contains that identity?
 
  • #4
Approximation? Square both sides of the equation (to get sin^2(x) + cos^2(x) - 2sin(x)cos(x) = 1 - sin(2x))? You're being much too vague ;)
 
  • #5
cos(x+y)=cos(x)cos(y)-sin(x)sin(y). Lety=45o. Net result
sin(x)-cos(x)=-sqrt(2)cos(x+y).

Is that simple enough?
 
  • #6
Originally posted by mathman
cos(x+y)=cos(x)cos(y)-sin(x)sin(y). Lety=45o. Net result
sin(x)-cos(x)=-sqrt(2)cos(x+y).

Is that simple enough?

Just nitpicking -- shouldn't that be

[tex]\sin(x)-\cos(x)=\sqrt{2}\cos(x+45)[/tex]
 
  • #7
Thanks everyone!
 
  • #8
need a help with log problem

I'm a bit confused with this problem can you help me to workout and explain it to me on the way. thanks.

log(e)x=a log(e0y=c express log(e){(100x^3y^-1/2)/(y^2)} in terms of a and c.

my interpretation is that you separate the function then workout by using loga(mn)=logam+logan law. thanks for your guys.
 
  • #9
Is it
[tex] \log(\frac{100x^3y^{\frac{-1}{2}}}{y^2})[/tex]
 
Last edited:
  • #10
jcm; you should start a new post when you want to ask an unrelated question.
 
  • #11
If I read your equations correctly, it should be ln100+3a-(5/2)c
 

FAQ: What simpler indentity is equal to sin(x) - cos(x)

What is the simpler identity for sin(x) - cos(x)?

The simpler identity for sin(x) - cos(x) is tan(x/2), also known as the half-angle formula for tangent.

How is tan(x/2) related to sin(x) - cos(x)?

The half-angle formula for tangent, tan(x/2), is derived from trigonometric identities involving sin(x) and cos(x), making it equivalent to sin(x) - cos(x).

Can tan(x/2) be simplified further?

No, tan(x/2) cannot be simplified further as it is already the simplest identity equivalent to sin(x) - cos(x).

In what cases is the use of tan(x/2) preferable over sin(x) - cos(x)?

Tan(x/2) is preferable over sin(x) - cos(x) when dealing with half-angle problems, when finding the value of an angle that is half of a given angle. It is also commonly used in integration and differentiation problems.

How can the half-angle formula for tangent be verified?

The half-angle formula for tangent, tan(x/2) = (sin(x))/(1+cos(x)), can be verified by using the double-angle formula for cosine, cos(2x) = 1 - 2sin^2(x), and substituting x/2 for x. This will result in tan(x/2) = (2sin(x/2)cos(x/2))/(1+cos(x)), which can be simplified to tan(x/2) = sin(x) - cos(x).

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