# Thread: Simplification of Trig Functions TWO

1. ## Simplification of Trig Functions TWO

Hi, I have

[(sin^2theta) - (cos^2theta) ]/ (sin(theta) + cos(theta))

And I need to simplify it to sin(theta) - cos(theta).

How do I do that? Thanks!

2. Originally Posted by classicstrings
Hi, I have

[(sin^2theta) - (cos^2theta) ]/ (sin(theta) + cos(theta))

And I need to simplify it to sin(theta) - cos(theta).

How do I do that? Thanks!
simply divide
for siplification, use sin(theta)=a;cos(theta)=b
you could divide only if a in not equal to b

Keep Smiling
Malay

3. So,

(a^2 - b^2)/ (a+b)

Right?

4. Originally Posted by classicstrings
So,

(a^2 - b^2)/ (a+b)

Right?
yes
you needn't use any trigonometric formulae here. It is simple algebraic division

Keep Smiling
Malay

5. Done thanks!

6. You can also factor, instead of long divsion.
$\displaystyle \frac{(\sin x+\cos x)(\sin x-\cos x)}{\sin x+\cos x}$

Originally Posted by malaygoel
you could divide only if a in not equal to b
You mean $\displaystyle a\not = -b$

7. Ah yes factoring, thanks for the 2nd opinion!

8. Originally Posted by classicstrings
Ah yes factoring, thanks for the 2nd opinion!
The interesting thing here is that Malay would not have suggested that
you simply divide if he had not already recognised that the numerator
factored from the difference of two squares form that it has and that
one of these factors was the denominator.

(At least that is my take on what was going on)

RonL