SOLUTION: Alright this is a trignometry identities question. The equation is tan^2x+1/tan^2x-1 = 1/sin^2x-cos^2x Now I need to make the left side equal the right side. I know that tan^2x

Question 1004983: Alright this is a trignometry identities question.
The equation is tan^2x+1/tan^2x-1 = 1/sin^2x-cos^2x
Now I need to make the left side equal the right side.
I know that tan^2x+1 is sec^2x or 1/cos^2x and the bottom tan changes to sin^2x/cos^2x -1 but I'm not sure what to do after that because I have a fraction over a fraction.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
it's actually easier to solve than you might think.

first recognize that 1 is equivalent to sin^2(x) + cos^2(x).

also recognize that tan^2(x) = sin^2(x) / cos^2(x).

you can either multiply numerator and denominator of the expression on the left by cos^2(x), or you can divide numerator and denominator of the expression on the right by cos^2(x).

working on the left:

your numerator of (tan^2(x) + 1) * cos^2(x) becomes:

tan^2(x) * cos^2(x) + 1 * cos^2(x) which becomes:

sin^2(x) + cos^2(x).

similarly, your denominator becomes sin^2(x) - cos^2(x).

working on the right:

your numerator of 1 becomes sin^2(x) + cos^(x).

(sin^2(x) + cos^2(x)) / cos^2(x) becomes:

sin^2(x) / cos^2(x) + cos^2(x) / cos^2(x) which becomes:

tan^2(x) + 1

similarly, your denominator becomes tan^2(x) - 1.

you are correct that tan^2(x) + 1 = sec^2(x), but that didn't really help you here, as far as i can tell.

RELATED QUESTIONS
I need help with verifying this trig identity. The problem is sec^4x-tan^4x / sec^2+... (answered by solver91311)

Decide whether the equation is a trigonometric identiye explain your reasoning.... (answered by lwsshak3)

thank you mr/mrs for helping me in advance. this website probably fell from heaven. i... (answered by stanbon)

Prove the identities: Sin^2x | Tan^2x/1+tan^2x Sin^4x+cos2x | Cos^4x... (answered by Alan3354)

Please Prove the following identities 1.) Tan (x/2) = tan (x)/sec (x) + 1 2.)... (answered by lwsshak3)

Verify: sec^2x-sin^2x-cos^2x = tan^2x Really need help on this. It breaks down as... (answered by lwsshak3)

I need help proving this trigonometric function. cos^2x + (tan^2x)(cos^2x)=1 (answered by stanbon,solver91311)

Please help me solve this equation: Which of the following is a valid trigonometric... (answered by lwsshak3)

I need help verifying these identities. {{{Sin(x)Cos(x)+Cos^2x =... (answered by Edwin McCravy)