# Homework Help: Help with Trigonometry

1. Sep 4, 2008

### ritwik06

1. The problem statement, all variables and given/known data
If $$tan x =\frac{2b}{a-c}$$
$$y=a.cos^{2} x + 2b.sin x.cos x+ c.sin^{2} x$$

$$z=a.sin^{2} x - 2b.sin x.cos x+ c.cos^{2} x$$

Prove y-z=a-c
3. The attempt at a solution

Assuming that the result to be proved is true;

y+z=a+c
and from the result to be proved
y-z=a-c
From this:
y=a
and
z=c

But can it be proved using the first equation of tan x ????? I tried a lot but i couldnt do it.

2. Sep 4, 2008

### Dick

Re: Trigonometry

Sure. Use the first equation to say 2b=(a-c)*tan(x). Substitute that for the 2b's in the other two equations.

3. Sep 4, 2008

### CompuChip

Re: Trigonometry

First of all, you cannot assume what you want to prove. For example, I can prove 1 = 0 that way:
Code (Text):
Assume that 1 = 0 (which we want to prove) is true.
Then also 0 = 1.
This is a true equation, QED
.

Secondly, if you assume y-z=a-c, then why do you conclude y = a and z = c and even if this where true (which it's not) how would this help the proof?

You will have to work from the given information. First work out what y - z is. Then you can use the first equation of tan(x) to replace b by something in terms of a, c and x. Finally, use some more trig identities to get to a - c.

4. Sep 5, 2008

### ritwik06

Re: Trigonometry

Thanks friend. It was silly of me to have not noticed that. Thanks a lot once again.