( 1 / tan x ) + tan x = 1 / ( sin x cos x )
We will start with the left side:
( 1 / tan x ) + tan x = ( 1 / sinx/cosx ) + ( sin x / cos x ) =
= ( cos x / sin x ) + ( sin x / cos x ) =
= ( cos² x + sin² x ) / ( sin x cos x ) =
= 1 / ( sin x cos x ) , which is same as the right side. The identity is proved.
Answer:
The system has infinite solutions described in the set 
Step-by-step explanation:
The augmented matrix of the system is
.
We apply row operations:
1. We add the first row to the second row twice and obtain the matrix ![\left[\begin{array}{cccc}-1&-1&-1&4\\0&-1&-2&10\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-1%26-1%26-1%264%5C%5C0%26-1%26-2%2610%5Cend%7Barray%7D%5Cright%5D)
2. multiply by -1 the rows of the previous matrix and obtain the matrix
that is the reduced echelon form of the matrix associated to the system.
Now we aply backward substitution:
1. Observe that the reduced echelon form has a free variable, then the system has infinite solutions.
2.

3.
.
Then the set of solutions is 
Yes, Two perpendicular lines
We want to put b alone on one side of the equation.
If we multiply by 1/2, we get 1/4bh = A/2. Not only did we not remove a variable from the left side, we made it even more complicated.
So the answer is A.