Plz help i do not understand the question.

Mathematics

1 answer:

gavmur [86]3 years ago

6 0

The question is asking you to come up with a real-life example of something that can be represented as 15+ c= 17.50. If I were you I would do sales tax. You bought an item with a 15 dollar price tag, but when you go to check out 2.50 are added in tax to equal 17.50. to solve subtract 15 from 17.50: c= 2.50. Your variable (c) represents the sales tax. Hope that helps! :)

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Use the identity tan(theta) = sin(theta) / cos(theta) to show that tan(???? + ????) = tan(????)+tan(????) / 1−tan(????) tan(????

VMariaS [17]

Answer:

See the proof below.

Step-by-step explanation:

For this case we need to proof the following indentity:

$tan(x+y) = \frac{tan (x) + tan(y)}{1- tan(x) tan(y)}$

So we need to begin with the definition of tangent, we know that $tan (x) =\frac{sin(x)}{cos(x)}$ and we can do this:

$tan (x+y) = \frac{sin (x+y)}{cos(x+y)}$ (1)

We also have the following identities:

$sin (a+b) = sin (a) cos(b) + sin (b) cos(a)$

$cos(a+b)= cos(a) cos(b) - sin(a) sin(b)$

Now we can apply those identities into equation (1) like this:

$tan (x+y) =\frac{sin (x) cos(y) + sin (y) cos(x)}{cos(x) cos(y) - sin(x) sin(y)}$ (2)

We can divide numerator and denominator from expression (2) by $\frac{1}{cos(x) cos(y)}$ we got this:

$tan (x+y) = \frac{\frac{sin (x) cos(y)}{cos (x) cos(y)} + \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{cos(x) cos(y)}{cos(x) cos(y)} -\frac{sin(x)sin(y)}{cos(x) cos(y)}}$