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

AI Thread Summary
The discussion focuses on simplifying the expression (sinx)^2 - (cosx)^2 over (sinx)^2 - (sinx cosx) using trigonometric identities. The user initially struggles to simplify the expression and seeks clarification on how the answer "1 + cotx" is derived. Suggestions include factoring the numerator as a difference of squares and multiplying both the numerator and denominator by 1/sin^2(x). Ultimately, the user reports success in understanding the simplification process. The conversation highlights the importance of applying fundamental trigonometric identities effectively.
Nishiura_high
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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!
 
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Nishiura_high said:

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)
 
Thanks. I got it now. :)
 

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