Is it anyone's biggest wish to show me step by step how to Verify this Trig identity?

i paid for a Mathway premium account to help me with this and it apparently can't. and they haven't replied to me about it either. so here are two examples of identities I have trouble verifying: (theta after every trig term in first one)

sin/ (1-cot)+ (cos)/ (1-tan) = (cos+sin)

sin (u+v)/ sin (u-v)= (tan (u)+ tan (v))/(tan (u)- tan (v))

Re: Is it anyone's biggest wish to show me step by step how to Verify this Trig ident

Quote:

Originally Posted by

**CoffeeBird** i paid for a Mathway premium account to help me with this and it apparently can't. and they haven't replied to me about it either. so here are two examples of identities I have trouble verifying: (theta after every trig term in first one)

sin/ (1-cot)+ (cos)/ (1-tan) = (cos+sin)

Part of you problem maybe that notation is all wrong.

Both $\displaystyle \cos~\&~\cos x$ are wrong. It should be $\displaystyle \cos(x)$.

We do not write $\displaystyle fx$ but we write $\displaystyle f(x)$. You see cosine is a function so use function notation.

$\displaystyle \frac{\sin(x)}{1-\tan(x)}=\frac{\sin(x)}{1-\frac{\sin(x)}{\cos(x)}}=\frac{\cos(x)\sin(x)}{ \cos(x) -\sin(x)}$

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Re: Is it anyone's biggest wish to show me step by step how to Verify this Trig ident

Re: Is it anyone's biggest wish to show me step by step how to Verify this Trig ident

@highvoltage

If you read reply #2, you will see that using $\displaystyle \cos \theta$ instead of $\displaystyle \cos( \theta)$ creates problems.

If you want to use any computer algebra system you will get an error message.

**Cosine is a **__function__, so the CAS expects you to use function notation.

So it is $\displaystyle \cos(\theta).$

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Re: Is it anyone's biggest wish to show me step by step how to Verify this Trig ident

Re: Is it anyone's biggest wish to show me step by step how to Verify this Trig ident

i should have specified, but i have been typing it in that way into the program. with the parentheses i mean. on mathway, i have made sure that i type everything as they show on their examples, and the server also tells me that it is correct but "cannot be answered automatically at this time". it does that for every single identity i type into it, and it says it has sent the problem to the developers but i haven't received a response ever. so, basically, i got ripped off.

Re: Is it anyone's biggest wish to show me step by step how to Verify this Trig ident

still trying to figure out how you got from step 2 to step 3 on the first one, but the second problem makes perfect sense now. thank you for posting the notes! : )

Re: Is it anyone's biggest wish to show me step by step how to Verify this Trig ident

Do you mean the step of putting the numerators over one, and then combining like terms in the denominators or the one after?

Re: Is it anyone's biggest wish to show me step by step how to Verify this Trig ident

oh i get it now...i was a little confused by the numerators being put over 1. thanks again, your answers have been very helpful