Question

solve: sin^2a-cos^2a/sin^2a-sinacosa

Answer 1

Is all of sin^2a - sinacosa in the denominator, or only the sin^2a part?

Answer 2

all of it

Answer 3

the numerator is the difference of 1 squares

the denominator .. find the common factor..

then you'll see what will cancel from the numerator and denominator

Answer 4

oops difference of 2 squares...

Answer 5

its a question about factoring

Answer 6

\[\frac{ \sin^{2}a - \cos^{2}a }{ \sin^{2}a - sinacosa }\] My first instinct is to factor the top. When you have something minus something, no matter what those somethings are, you can factor it like a difference of squares:

\[(x-a) = (\sqrt{x} - \sqrt{a})(\sqrt{x}+\sqrt{a})\]

So thats what im going to do with the top.

Answer 7

\[\frac{ (sina-cosa)(sina+cosa) }{ \sin^{2}a-sinacosa }\]Now I can factor a sin out of the bottom:

\[\frac{ (sina-cosa)(sina+cosa) }{ sina(sina-cosa) }\]Now you have a top and bottom factor that cancel:

\[\frac{ sina + cosa }{ sina } = \frac{ sina }{ sina }+\frac{ cosa }{ sina }= 1 + cota\]

Answer 8

aghh thank you. that actually helped a lot.

Answer 9

Yeah, sure :3