# An expression equivalent to [cos(x)+sin(x)]/[cos(x)+sin(x)]

1. Feb 9, 2005

### aisha

I have this question --> $$\frac {\cos (x) + \sin (x)} {\cos (x) - \sin (x)}$$ how do you find an expression that is eqivalent to this using trig identities? I have no clue every time I do this problem the top and bottom cancel out plus none of the terms can be replaced with trig identities, can somone plz help me out ?

2. Feb 9, 2005

### Galileo

You could multiply the top and bottom by cos x+sin x.
Then use some trig identities like $\sin^2x+\cos^2x=1$ upstairs and downstairs. Then you can simplify is further by using 2 other trig id's.
Look up the table. :)

3. Feb 10, 2005

### aisha

Can I ask what table?

4. Feb 10, 2005

### xanthym

Try what the previous msg suggested:
a) Multiply Numerator & Denominator by:
$$cos(\theta) + sin(\theta)$$
b) Use Identities Like:
$$sin^2(\theta) + cos^2(\theta) = 1$$
$$sin(2\theta) = 2sin(\theta)cos(\theta)$$
$$cos(2\theta) = cos^2(\theta) - sin^2(\theta)$$
Also check the following Trig Identity Table:
http://www.math2.org/math/trig/identities.htm

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5. Feb 10, 2005

### primarygun

why not try tan ?

6. Feb 10, 2005

### xanthym

Yes. The tan() and sec() would be next. (Needed to leave something for the reader to discover!!)

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Last edited: Feb 10, 2005