Answer:
The answer to your question is below
Step-by-step explanation:
csc α - cot α = 
Work with the left part

Simplify

Multiply by the reciprocal
Simplify

Remember that
sin²α = 1 -cos²α
Substitute the previous equation

Simplify
The identity i proved.
Answer:
Horizontal Asymptote: y=2
Vertical Asymptote: x=3
Step-by-step explanation:
One way: Look at graph
Look at for a horizontal or vertical line that both lines don't touch.
Second Way:
When you look for vertical asymptotes, you set the denominator equal to zero and solve.
For example, the second question has a denominator of x-3.
x-3=0
x=3 (This is the vertical asymptote)
When you look for horizontal asymptote, you do long division.
For example, the first question 
The answer will be 2. 2 is the quotient. You only want quotient not remainder.
y=2.
The graph described is the graph of a quadratic function.
The x-intercept of the function is at; (8, 0).
<h3>What type of function is described by the graph?</h3>
It follows from the description box of the graph that it begins in the third quadrant, and rises through a series of points in the first quadrant before it exits the first quadrant.
Hence, it follows that the graph is a quadratic function and its x-intercept is at point; (8,0).
Read more on intercept;
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The length of the hypotenuse will be equal to H=122.25 when value of x=14.
<h3>What is pythagorean theorem?</h3>
Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal the square of the sum of the other two sides.
It is given that:
Value of x=14
The perpendicular is =6x+5=6x14+5=89
The base is =6x=84
So by using the Pythagorean theorem:-

Hence the value of hypotenuse will be H=122.25
To know more about the Pythagorean theorem follow
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The first one is 212
and the second one is 158
so yes it is false they do not equal