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Makovka662 [10]
2 years ago
5

Students were asked to prove the identity (sec x)(csc x) = cot x + tan x. ​

Mathematics
1 answer:
pogonyaev2 years ago
8 0

Let's prove that (sec x)(csc x) is equal to cot x + tan x

\Longrightarrow  \sf (sec(x) )(csc(x))

\Longrightarrow  \sf \dfrac{1}{\cos \left(x\right)\sin \left(x\right)}

\Longrightarrow  \sf \dfrac{\cos ^2\left(x\right)+\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}

\Longrightarrow  \sf \dfrac{\cos ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)} + \dfrac{\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}

\Longrightarrow  \sf \dfrac{\cos\left(x\right)}{\sin \left(x\right)} + \dfrac{\sin \left(x\right)}{\cos \left(x\right)}

\Longrightarrow  \sf cot(x)  + tan(x)

Hence student A did correctly prove the identity properly.

Also Looking at student B's work, he verified the identity properly.

So, Both are correct in their own way.

<h3>Part B</h3>

Identities used:

\rightarrow \sf sin^2 (x) + cos^2 (x) = 1       (appeared in step 3)

\sf \rightarrow \dfrac{cos(x) }{sin(x) }  = cot(x)               (appeared in step 6)

\rightarrow \sf \dfrac{sin(x )}{cos(x) }  = tan(x)               (appeared in step 6)

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I broke down the fraction entirely.

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3 years ago
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AB (the notation usually uses a double arrow in top of the letters)

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For example, we can choose the line AB and the point D, that does not belong to the line.

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3 years ago
Lucy’s rectangular garden is 15ft long and 12 ft wide. She adds a right triangle to her garden plan, so that the triangle’s heig
KIM [24]
Okay, so lets break this down.

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Okay, now time for the triangle.  The way that it words it may be confusing but I can draw you a picture of what it looks like (its a quick draw so it looks kinda bad).

But, for the triangle we are going to extend the 12ft line (shorter side; width) and create a line that is 7 feet long.  Then, we are going to find the midpoint of the 15ft side and connect that with the end point of the triangle.

Since its on the longer side and its the midpoint, the triangle is going to have a base of 7.5ft (half of 15).  Then, the height is 7ft as included in the question.

Now to solve the area of a right triangle, you can use 1/2(bh).  So 1/2 of the base times height.

This is 1/2 of (7.5*7) which is 1/2(52.5) and finally the area of the triangle is 26.25ft².

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4 0
3 years ago
&lt;17 and &lt;18 are vertical angles. m &lt;17=(5x+3)(degrees) and m&lt;18=(3x+23)(degrees) find the measure of &lt;18
UNO [17]
I think c is the answer to ur question
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3 years ago
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Oksana_A [137]

Answer:

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Step-by-step explanation:

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f(-10) = 200 - 10 - 4

f(-10) = 186

4 0
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