Use the basic identities to change the expression to one involving only sines and cosines. Then simplify to a basic trig function.

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Step-by-step explanation:

First, convert all the secants and cosecants to cosine and sine, respectively. Recall that and .

Thus:

Let's do the first part first: (Recall how to divide fractions)

For the second term:

So, all together: (same denominator; combine terms)

Note the numerator; it can be derived from the Pythagorean Identity:

Thus, we can substitute the numerator:

Everything simplifies to 1.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

25

step-by-step explanation: