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Need help simplifying trigonometric expression

G

Gusty987

Golden Member
Had this in highly technical...someone said it was "not appropriate" for that forum.

I have the following problem...

cos^2(x)
_______
1+sin(x)

...which I know simplifies to...

1-sin(x)

...I need to know how that was simplified! I will owe a deep debt of gratitude for anyone who can explain this to me!
 
Originally posted by: Gusty987
But how do you get around the "+" in the denominator? Could someone explain that in English?
Click to expand...

after some manipulation you get: (1+sin)(1-sin)/(1+sin)

(1+sin) is a factor by itself. you don't need to be concerned with the +. you can cancel (1+sin) from both the top and the bottom
 
Originally posted by: Gusty987
you can cancel (1+sin) from both the top and the bottom
Click to expand...

I think thats the part I dont get.
Click to expand...

well in (1+sin)(1-sin)/(1+sin), on the top level of operations you can see you only have multiplications and divisions. what's inside the parenthesis can be treated as integral parts on this level. so if you set

a = 1+sin
b = 1-sin

you have a*b/a

get it?
 
or just very simple. lets make (1+sin) = 4, (1-sin) = 3. so you basically get:

4 * 3 / 4 = 12 / 4 = 3.

Now notice, you can cancel out the 4 and the 4, which leaves you with the same thing, 3. (1+sin) in the numerator cancels out with the (1+sin) in the denominator 🙂

edit: forget about the X, don't notice it at first. after u get (1+sin)(1-sin)x / (1+sin)x, the (1+sin)x cancels out with the (1+sin)x... leaving u with (1-sin)x...
 
Originally posted by: icejunkie
or just very simple. lets make (1+sin) = 4, (1-sin) = 3. so you basically get:

4 * 3 / 4 = 12 / 4 = 3.

Now notice, you can cancel out the 4 and the 4, which leaves you with the same thing, 3. (1+sin) in the numerator cancels out with the (1+sin) in the denominator 🙂

edit: forget about the X, don't notice it at first. after u get (1+sin)(1-sin)x / (1+sin)x, the (1+sin)x cancels out with the (1+sin)x... leaving u with (1-sin)x...
Click to expand...


How do you get (1+sin)(1-sin)x from cos^2 x in the numerator?
 
Originally posted by: Gusty987
Originally posted by: icejunkie
or just very simple. lets make (1+sin) = 4, (1-sin) = 3. so you basically get:

4 * 3 / 4 = 12 / 4 = 3.

Now notice, you can cancel out the 4 and the 4, which leaves you with the same thing, 3. (1+sin) in the numerator cancels out with the (1+sin) in the denominator 🙂

edit: forget about the X, don't notice it at first. after u get (1+sin)(1-sin)x / (1+sin)x, the (1+sin)x cancels out with the (1+sin)x... leaving u with (1-sin)x...
Click to expand...


How do you get (1+sin)(1-sin)x from cos^2 x in the numerator?
Click to expand...

cos^2 = 1 - sin^2 <-- That's a rule. You SHOULD know that.

1 - sin^2 = (1+sin)(1-sin) <-- simple foiling I think it's called (not good with English math terms)...

do the math man. (1+sin)(1-sin) = 1 - sin + sin -sin^2.... = 1 - sin^s....
 
Originally posted by: dighn
Originally posted by: Gusty987

get it?
Click to expand...

NO!
Click to expand...

ok..

would you not agree that

(1+x)(1-x)/(1+x) is equivalent to ab/a
if a is (1+x) and b is (1-x)?

then would you not agree that ab/a simplifies to ab/a = b = 1-x?
Click to expand...

Yes I understand this. The same thing in the numerator and denominator simply cross out. But in the expression I gave, how do you get it into the ab/a form from a/1+b?

 
If you don't realize that (cosx)^2+(sinx)^2=1... then you need to start paying attention in your trig class.

And if you don't know that x^2-y^2 = (x-y)(x+y)... then you should've paid attention in your algebra class.
 
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