Solving Trigonometric Proofs: Struggling with Two Challenging Examples

[mrtkawa]

i need help for these 2 trig proofs, i did everything i could but it's impossible.

1st question; (cot^2X)-1=csc^2X

and

2nd question; (cot^2X)-(cos^2X)=cos^2Xcot^2X

caution, both might be insoluable

thanks!

 

[z-component]

You can use the Pythagorean Identities to evaluate the expressions to see if they are equal. Recall that $$\cos^{2} \theta + \sin^{2} \theta = 1$$ and that you can modify this equation by dividing by sin or cos to give two additional equations in terms of tan, cot, sec, and csc.

 

[0rthodontist]

Do you know the identity sin^2(x) + cos^2(x) = 1? Try dividing, rearranging terms, etc.

 

[mrtkawa]

i tried everything but it does not work at all!

 

[z-component]

You need to use the identity we've given you. Divide the identity by sin x and see what you come up with. You should have something in terms of cotangent and cosecent.

 

[mrtkawa]

oh i forgot tell you that my ass hole teacher want to us to do the proof by solving either side
so i can not divide, square, multiply or anything to the both side or the one side

 

[z-component]

I know and what I'm trying to get you to do is complete this one step so you can compare the result to your first question. What do you get when you divide the identity above by sin x?

 

[VietDao29]

I am going to give you an example, which is nearly the same as this one:
Example:
Prove that:
sec²x = tan²x + 1
I am going from the LHS to the RHS:
$$\sec ^ 2 x = \frac{1}{\cos ^ 2 x} = \frac{\sin ^ 2 x + \cos ^ 2 x}{\cos ^ 2 x} = \tan ^ 2 x + 1$$ (Q.E.D)
-------------------
By the way, your first problem is not correct, it should read:
cot²x + 1 = csc²x
not
cot²x - 1 = csc²x
-------------------
For the second problem, what's cot²x in terms of sin(x), and cos(x)? You should also note that:
sin²x + cos²x = 1 (the Pythagorean Identity)
Can you go from here? :)