How Do You Simplify Trigonometric Expressions Using Identities?

[asdfsystema]

Trigonometry Basic (URGENT) please help !

Homework Statement

SIMPLIFY:
sin(x)/cot^2(x) - sin(x)/cos^2(x)

Homework Equations

Trigonometric identities I think

The Attempt at a Solution

I got sin(x)cot^-2(x) - sin(x) sec^2(x) ...

but the book says the answer is -sin(x).


Any starting points please? Thanks

 

[meiso]

First try changing the cot^2(x) expression into an expression in terms of sin(x) and cos(x), and leave everything in terms of sin(x) and cos(x), i.e. don't change the cosine expression in the right term into a secant expression.
As you've suspected, you will need to use trigonometric identities to aid in your simplification.

Hint: You should know the trigonometric identity tan(x) = sin(x)/cos(x). Try to take it from there.

After you've done that, try simplifying the entire expression into one fraction, still in terms of just sin(x) and cos(x).
I'll tell you that you will need to know at least one more trigonometric identity after you've gotten it simplified to a single fraction to complete the problem.

 

[asdfsystema]

I'm not sure where to apply the trig identity.

I got sin(x)/ (cos(x)/sin(x))^2 - sin(x)/ cos(x)*cos(x)

Where does the identity come into play?

Thanks for the quick response

 

[meiso]

I'm not sure where to apply the trig identity.

I got sin(x)/ (cos(x)/sin(x))^2 - sin(x)/ cos(x)*cos(x)

Where does the identity come into play?

Thanks for the quick response

Ok, you applied the first trig identity cot(x) = cos(x) / sin(x) correctly. You need to clean this expression up a bit before you will be able to apply another identity. Combine the powers of sine and cosine in both terms, and see what the denominators will become. Remember if you are adding or subtracting two fractions with the same denominator, you may combine them into one fraction with that same denominator.

Hints: In any expression, (a/b) / (c/d) = (a/b) * (d/c)
Also, (a/c) + (b/c) = (a+b)/c
With trig expressions, they work the same as multiplying other expressions with identical bases, so for example
sin^4(x) * sin(x) = sin^5(x)