Calculus Help for University Students: Proving Identities and Solving Equations

[chowder]

Hello everyone!

I'm entering my first year of university calculus, and I must say, I was never really good with math. So I have a few questions. This will seem pathetic to some of the math wizzards!

1.) Show that the identity 1+cot^2 ϑ = csc^2 ϑ

follows from

sin^2 ϑ + cos^2 ϑ = 1.


2.) Solve sec^2 x = √3 tan x + 1 on [0, π)



Thanks for your help!

 

[quasar987]

Hi chowder,

you must show some work to get help.

what have you tried? what are your thoughts, etc.

 

[VietDao29]

Hello everyone!

I'm entering my first year of university calculus, and I must say, I was never really good with math. So I have a few questions. This will seem pathetic to some of the math wizzards!

1.) Show that the identity 1+cot^2 ϑ = csc^2 ϑ

follows from

sin^2 ϑ + cos^2 ϑ = 1.


2.) Solve sec^2 x = √3 tan x + 1 on [0, π)



Thanks for your help!

In case you have no idea to start off the problem, the first problem can be done by relating the cot, and csc functions to the sin, and cos functions, since you need to use the Pythagorean Identity to prove this one.
For the second problem, can sec²x be rewritten in terms of tan(x)?
$$\ces ^ 2 x = \frac{1}{\cos ^ 2 x} = \frac{\sin ^ 2 x + \cos ^ 2 x}{\cos ^ 2 x} = ...$$
-----------------
Ok, can you go from here? :)