# trig

posted by .

simplify the expression.

cos^2x+sin^2x/cot^2x-csc^2x

• trig -

Parentheses are assumed missing. Implied parentheses are ALWAYS required in numerator and denominator of fractions.

(cos^2x+sin^2x)/(cot^2x-csc^2x)

This problem can be solved by converting all functions in terms of sine and cosine according to the standard definitions.

(cos^2x+sin^2x)/(cot^2x-csc^2x)
=(cos^2(x)+sin^2(x))/(cos^2(x)/sin^2(x)-1/(sin^2(x))

Use sin²(u)+cos²(u)=1 to reduce the numerator to 1.
Since the denominator has a common factor of sin²(x), we can simplify that too!

=(1)/[(cos²(x)-1)/sin²(x)]
=sin²(x)/(cos²(x)-1)
=sin²(x)/(-sin²(x)
=-1

## Similar Questions

2. ### Trigonometry

Hello all, In our math class, we are practicing the trigonometric identities (i.e., sin^2(x)+cos^2(x)=1 or cot(x)=cos(x)/sin(x). Now, we are working on proofs that two sides of an equation are equal (for example, sin(x)*csc(x)=1; sin(x)csc(x)=sin(x)/sin(x)=1; …
3. ### verifying trigonometric identities

How do I do these problems? Verify the identity. a= alpha, b=beta, t= theta 1. (1 + sin a) (1 - sin a)= cos^2a 2. cos^2b - sin^2b = 2cos^2b - 1 3. sin^2a - sin^4a = cos^2a - cos^4a 4. (csc^2 t / cot t) = csc t sec t 5. (cot^2 t / csc
4. ### Math - Trig

I'm trying to verify these trigonometric identities. 1. 1 / [sec(x) * tan(x)] = csc(x) - sin(x) 2. csc(x) - sin(x) = cos(x) * cot(x) 3. 1/tan(x) + 1/cot(x) = tan(x) + cot(x) 4. csc(-x)/sec(-x) = -cot(x)
5. ### trig 30

For csc^2 A-1/cot A csc A, what is the simplest equivalent trig expression?
6. ### Math

cos(tan + cot) = csc only simplify one side to equal csc so far I got this far: [((cos)(sin))/(cos)] + [((cos)(cos))/(sin)] = csc I don't know what to do next
7. ### trig

For each expression in column I, choose the expression from column II to complete an identity: Column I Column II 1. -tanxcosx A. sin^2x/cos^2x 2. sec^2x-1 B. 1/sec^2x 3. sec x/cscx C. sin(-x) 4. 1+sin^2x D.csc^2x-cot^2x+sin^2x 5. …
8. ### trig

simplify the expression. (sin^2x+cos^2x) - (csc^2x-cot^2x)
9. ### Pre-Calculus

Prove that each equation is an identity. I tried to do the problems, but I am stuck. 1. cos^4 t-sin^4 t=1-2sin^2 t 2. 1/cos s= csc^2 s - csc s cot s 3. (cos x/ sec x -1)- (cos x/ tan^2x)=cot^2 x 4. sin^3 z cos^2 z= sin^3 z - sin^5 …
10. ### Pre-Calculus

I don't understand,please be clear! Prove that each equation is an identity. I tried to do the problems, but I am stuck. 1. cos^4 t-sin^4 t=1-2sin^2 t 2. 1/cos s= csc^2 s - csc s cot s 3. (cos x/ sec x -1)- (cos x/ tan^2x)=cot^2 x …

More Similar Questions