Melody

You need to use brackets - the meanings are far from clear

$$\\\frac{sec 3\pi}{7}\\\\
=\frac{sec \pi}{7}\\\\
=\frac{1}{7cos\pi}\\\\
=\frac{1}{7*-1}\\\\
=-\frac{1}{7}\\\\$$

WOW heureka, you gave yourself something to chew on there!    

My answer is no where near as impressive.   

sinx=cosx          When cosx=0,    sinx ≠0     so    cosx ≠ 0  therefore I can divide by it.

$$\\\frac{sinx}{cosx}=1\\\\
tanx=1\\\\
$tan is pos in the 1st an 3rd quad$\\\\
x=\frac{\pi}{4},\;\;\frac{5\pi}{4}\;\;etc\\\\
x=n\pi+\frac{\pi}{4}\qquad n\in Z\qquad$ (n is an integer)$$

anon is correct but i is an imaginary number.

There are no real solutions because no real number squared = a negative number.

$$\\(0.569e^{-r*3})+(0.559e^{-r*4})=1\\\\
(0.569e^{-3r})+(0.559e^{-4r})=1\\\\$$

Before I go any further, are you sure those 2 coefficients aren't supposed to be the same?

there are no super neat solutions for this

Use  [2nd]

"1st you dumbass"      That is just priceless.     ROF LOL        

Yes, your teacher will probably get the answers correct :)

Thanks Heureka,