Question

BRAINLIESTTT ASAP! PLEASE HELP ME :)

Answer 1

Answer: Choice A

Only the second equation is an identity

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Explanation:

When it comes to ugly equations like this, I find that graphing will help determine if we have an identity or not (so we don't waste time trying to prove something is an identity when in reality it is not).

How does it work? Well all we do is graph each side as its own equation. Use x in place of theta.

For problem 1, you'll have $f(x) = 6\frac{\cot^2(x)}{csc(x)}\sec^2(x)$and $g(x) = 9\tan(x)\cos(x)\csc^2(x)$ as shown in figure 1 (see attached image below). As you can see, the two graphs do not line up perfectly. So we do not have an identity for equation 1.

We can use numerical methods to find a counter example. Let's say we try plugging in x = pi/3 into both f(x) and g(x). We should get the same value if we had an identity, however

f(pi/3) = 6.93

g(pi/3) = 10.39

which is one counter example to show that f(x) = g(x) is not true for all x, therefore we don't have an identity.

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The equation in problem 2 is an identity. Graph

$f(x) = 9\frac{\cot^2(x)}{\csc(x)}\sec^2(x)$

$g(x) = 9\csc(x)$

and you'll find the two graphs lining up perfectly. In figure 2, the blue dashed curve is over top the red solid line giving the illusion we have a single curve that is colored with blue and red stripes.

Figure 3 shows the steps on how to algebraically prove we have an identity here. Notice that all of the steps in figure 3 have the right hand side (RHS) remain the same the entire time. Only the left hand side (LHS) is being altered and transformed into the RHS.

Answer 2

Answer:

none of the equations are identities, I think.