Homework Help: Use trig identities to simplify an expression (has sins and cosines)

1. Apr 28, 2012

Nishiura_high

1. The problem statement, all variables and given/known data

Use fundamental identities to simplify the expression:

(sinx)^2 - (cosx)^2
____________________
(sinx)^2 - (sinx cosx)

*note: it's a numerator and denominator. The underscore line is the fraction line.

*note: The answer in the back of the book is "1 + cotx" but I would like to know how it got there.

2. Relevant equations

(sinx)^2 + (cosx)^2 = 1

other trig identities

3. The attempt at a solution

(sinx)^2 - (cosx)^2
_________________
sinx(sinx - cosx)

I factored out sinx out of the bottom, but I don't really see any identies that would simplify sinx-cosx. (I have a chart of identities.) I tried to simplify the top using the relevant identity I already listed.

Thanks for any help!

Last edited: Apr 28, 2012
2. Apr 28, 2012

SammyS

Staff Emeritus
Factor the numerator as a difference of squares.

or ...

Starting with the original expression, multiply the numerator and denominator by 1/sin2(x)

3. Apr 29, 2012

Nishiura_high

Thanks. I got it now. :)