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

[Nishiura_high]

Homework Statement

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.

Homework Equations

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

other trig identities

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!

 

[SammyS]

Homework Statement

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.

Homework Equations

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

other trig identities

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!

Factor the numerator as a difference of squares.

or ...

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

 

[Nishiura_high]

Thanks. I got it now. :)