# Thread: Need help proving trigonometric identities?

1. ## Need help proving trigonometric identities?

1.) cot^2x=(cscx-1)(cscx+1)

2.) tan^2x=sec^2x-sin^2x-cos^2x

3.) csc^3xtan^2x=cscx(1+tan^2x)

4.) sinx/1-cosx + sinx/1+cosx = 2cscx

5.) sinx/cscx-1 + sinx/cscx+1 = 2tan^2x

2. ## Re: Need help proving trigonometric identities?

Originally Posted by ccfoose
1.) cot^2x=(cscx-1)(cscx+1)

2.) tan^2x=sec^2x-sin^2x-cos^2x

3.) csc^3xtan^2x=cscx(1+tan^2x)

4.) sinx/1-cosx + sinx/1+cosx = 2cscx

5.) sinx/cscx-1 + sinx/cscx+1 = 2tan^2x

1.
\displaystyle \begin{align*} \left(\csc{x} - 1\right)\left(\csc{x} + 1\right) &\equiv \csc^2{x} - 1 \\ &\equiv \cot^2{x} \end{align*}

2.
\displaystyle \begin{align*} csc{x}\left(1 + \tan^2{x}\right) &\equiv \csc{x}\sec^2{x} \\ &\equiv \frac{1}{\sin{x}}\cdot \frac{1}{\cos^2{x}} \\ &\equiv \frac{1}{\sin{x}\cos^2{x}} \\ &\equiv \frac{\sin^2{x}}{\sin^3{x}\cos^2{x}} \\ &\equiv \frac{1}{\sin^3{x}} \cdot \frac{\sin^2{x}}{\cos^2{x}} \\ &\equiv \csc^3{x}\tan^2{x} \end{align*}

Trigonometric identities just take a bit of playing around. I'll leave you to try the rest.

3. ## Re: Need help proving trigonometric identities?

i know how to do most of them, i just didnt understand these beacuse some some seemed too simple and or too complex. like 4 and 5, i dont understand at all!

4. ## Re: Need help proving trigonometric identities?

Originally Posted by ccfoose
i know how to do most of them, i just didnt understand these beacuse some some seemed too simple and or too complex. like 4 and 5, i dont understand at all!
Since you haven't used brackets, I'm not exactly sure what your equations are, but I would suggest with 4 and 5 to start by getting a common denominator on the LHS.

5. ## Re: Need help proving trigonometric identities?

its like the first part is one fraction, then plus the second fraction... i always mix up my common denominators, so i was just wondering how exactly to do probems like those.

6. ## Re: Need help proving trigonometric identities?

Originally Posted by ccfoose
its like the first part is one fraction, then plus the second fraction... i always mix up my common denominators, so i was just wondering how exactly to do probems like those.
Getting a common denominator is simple.

\displaystyle \begin{align*} \frac{a}{b} + \frac{c}{d} = \frac{ad}{bd} + \frac{bc}{bd} = \frac{ad + bc}{bd} \end{align*}

You won't learn anything until you try some things for yourself.

7. ## Re: Need help proving trigonometric identities?

can you do one of the ones using fractions so i can know the whole process, then i can try the other

8. ## Re: Need help proving trigonometric identities?

Originally Posted by ccfoose
can you do one of the ones using fractions so i can know the whole process, then i can try the other
Please don't post more than two questions in a thread. Otherwise the thread can get convoluted and difficult to follow. See rule #8: http://www.mathhelpforum.com/math-he...hp?do=vsarules.

Post one of these questions that you think getting help on will be of benefit in doing the others. Also, please show some effort - show all your work and say where you get stuck.