Idenities

[Gimlin]

Could someone list the techniques needed to solve identities

Thanks

[noble]

Gimlin,
I'm assuming you mean you want to use identities to simplify
an equation or system.....

The idea of using trig identities is putting an equation or system
into a form that's easier to work with. What a lot of people
(including myself) tend to suggest is to put the equation or
system into terms of sin and cos and then see which terms can be
neglected or cancelled out of the equation.

Some of the most basic identities needed by anyone who
wishes to simplify an equation can be found on the following
website (among many others just do a search for 'trig identities')

http://www.hoxie.org/Math/trig/identities.htm

When you're presented with an equation, there are many ways
to approach it. The fundamental idea, however, is to see
how an identity can be used to simplify it and then rearrange and
manipulate the equation to suit it.

e.g.:

(sin x + cos x)/(sin 2x)

in order to solve this, you would first spot the sin 2x in the
denominator and see that (sin 2x) can also be rewritten as
(2*sin x * cos x )

if you replace the sin2x with it's counterpart you would get the
following:

(sin x + cos x)/(2*sin x * cos x)

You can further rearrange this equation to:

(sin x)/(2*sin x * cos x) + (cos x)/(2*sin x * cos x)

if you cancel out the (sin x)/(sin x) in the first half of the equation
and the (cos x)/(cos x) in the second part, you will have the
following:

(1/2)(sin x + cos x)


This is just one simple example of how using trig identities can
simplify one equation into something much easier to work with.

Finally, to answer your question fully, first you want to see where
an identity can be used and replace that part of the equation with
the identity and continue this until you believe the equation is in
its simplest form.
Sometimes, this is a trial and error process and with more
complicated systems and equations this can be difficult. With
practice, the simplification will become second nature and will
greatly help you in other areas of math down the road.

Listen to anyone who tells you to memorize the basic identites!

If you have more questions or would like a more complicated
example, plz feel free to ask.

[RAEsquivelC]

term, with an = between them. The procedure to prove the identity consisted in manipulating only the right-hand side of the equation, until it was identical to the left-hand side, hence the name, identities. Am I right, or has modern math changed that much?

[nishantp]

No, I was taught this stuff just a few months ago. You have to prove that the left equals the right. Its easier to break things down than build them up, but it's not always possible. There's no foolproof technique. You just have to practice a lot.


Besides...all this stuff isn't really modern...it's all centuries old.

[sql_lall]

I believe many people would be willing to help, but first may i suggest you post specific questions, or possible an area (like 'trigonometry' or 'quadratic equations' or 'geometric series etc)

If you were talking about trig identities, noble covered a lot
however, if it is other types, then do you have an example question?