SOLUTION: How do you solve trigionomic identies?

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Question 254148: How do you solve trigionomic identies?
Found 2 solutions by richwmiller, Edwin McCravy:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
First, your question is hard to understand because you spelled most of it incorrectly.
And secondly your question is like asking how do you do math.
Be specific about which identities you want to discuss.
Identities are not problems. They are used to solve problems.

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
How do you solve trigionomic identies?


1. Be very proficient in doing algebra.

2. Know all your trig identities:

The reciprocal identities:

sec%28A%29+=+1%2Fcos%28A%29
csc%28A%29+=+1%2Fsin%28A%29
cot%28A%29+=+1%2Ftan%28A%29

The quotient identities

tan%28A%29=sin%28A%29%2Fcos%28A%29
cot%28A%29=cos%28A%29%2Fsin%28A%29

The Pythagorean identities 

Sin%5E2A+%2B+Cos%5E2A+=+1 
i+%2B+Tan%5E2A+=+Sec%5E2A
1+%2B+Cot%5E2A+=+Csc%5E2A

as well as all of their rearrangements:

Sin%5E2A+=+1+-+Cos%5E2A
Cos%5E2A+=+1+-+Sin%5E2A
Tan%5E2A+=+Sec%5E2A-1
Cot%5E2A+=+Csc%5E2A-1

Also recognize factors of the Pythagorean
identities which can be written as the
difference of two perfect squares, such
as recognizing that since

1+-+Cos%5E2A+=+%281-Cos%28A%29%29%281%2BCos%28A%29%29
1+-+Sin%5E2A+=+%281-Sin%28A%29%29%281%2BSin%28A%29%29
Sec%5E2A-1+=+%28Sec%28A%29-1%29%28Sec%28A%29%2B1%29
Csc%5E2A-1+=+%28Csc%28A%29-1%29%28Csc%28A%29%2B1%29

that when one of the factors on the right
appears, that you can multiply top and bottom 
by another factor and a Pythagorean identity 
will arise.


3.  Work with the most complicated side first.
    Then when you have simplified it as far
    as you can, and the identity has not
    been solved, begin to work with the other
    side to see if you can get it to an equivalent
    form.

4.  If you are stuck, try using the reciprocal and
    quotient formulas so that only sines and cosines
    appear. 

Edwin