Need help w/ proving identities, factoring, etc.

[clarke0581]

1. Use graphs to prove whether the following equation could possibly be an identity, or determine it is definitely not an identity: cos T (pie/2 + 1)= -sin T

2. Factor and simplify
a) tan2 t – cos2 t
b) csc4 t + 4 csc2 t – 5

3. Prove the identity: tan x csc x = sec x

4. State whether or not the following three equations are an identity. If it is, prove it.
a) sec4 x – tan4 x = 1 + 2 tan2x
b) cos2 x (sec x + 1)2 = (1 + cos x)2
c) 1+ cos c/sin X + sin x/ (1 +cos x) = 2 csc x

5. Prove log10(cot x) = -log10(tan x)

6. Prove the following: cos (x + pie) = cos x

7. Prove cos x sin y = 1/2 (sin(x + y) – sin (x - y))

 

[nezenic]

For the first question, I would just plot both sides and see if they are identical or not.

 

[clarke0581]

I am not sure how to even began to do that. I am just not understanding it.

 

[tkhunny]

First) You should try to remember your algebra. Algebra is an important prerequisite and this is an excellent problem set to demonstrate why.

cot(x) = 1/tan(x) = [tan(x)]^(-1)

Now, what do you know about logarithms and exponents?

You should be able to figure out #5 without any further trouble.

A difference of squares goes like this when factored:

x^2 - y^2 = (x+y)(x-y)

You should be able to do 2a without any further difficulty.

A nice trinomial can be factored simply:

x^2 + 4x - 5 = (x+5)(x-1)

You should be able to do 2b without any further difficulty.

We ahven't even used any trig, yet, except cot(x) = 1/tan(x) and we're well on our way to the completion of the problem set.

Second) "Pie" is for eating. "Pi" is for math.

 

[clarke0581]

Thanks, there a total of 15 questions and I was able to do excempt for these. Not sure if someone can show me step by step on how to proceed with the last 6 questions.

 

[tkhunny]

Well, since I just directed you through two of the SEVEN and you just ignored it, it seems to me that you just want someone to do your homework.

Plus, if the ones you can't do just happen to be numbered consecutively, starting at 1, it seems to me that you just want someone to do your homework.

I must conclude, then, that you have shown no effort whatsoever. Let's see what you can do.

 

[clarke0581]

WOW.. not true. ....

 

[tkhunny]

Great! I would LOVE to be entirely wrong. Prove it to be so.

Let's see what you can do.

Start with #3. It is patently trivial. If you can't do that one, you are in the wrong class and you need far more help than can be offered without a complete refresher course in basic algebra and trigonometry.

I'll even give you a hint: tan(x) = sin(x)/cos(x)

Now, go, prove me wrong in my previously poorly refuted assumptions.