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2 years ago

Select the type of equations. consistent equivalent Inconsistent

Mathematics

1 answer:

KatRina [158]2 years ago

6 0

The type of equation is (a) consistent equations

<h3>How to determine the type of equation?</h3>

The attached figure completes the question

From the graph, we can see that the two lines are not parallel and they do not represent the same line

This means that the lines are consistent

Consistent lines produce consistent equations

Hence, the type of equation is (a) consistent equations

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2.) Fill in the blank.

Montano1993 [528]

Answer:

E.) 1

Step-by-step explanation:

Firstly we will solve for L.H.S.

L.H.S. = $Csc^2\theta$

Since we know that $Csc^2\theta$ is the inverse of $Sin^2\theta$ .

So we can say that;

$csc^2\theta=\frac{1}{sin^2\theta}$

Now For R.H.S.

$Cot^2\theta+1$

Since we can rewrite $cot^2\theta$ as $\frac{cos^2\theta}{sin^2\theta}$ .

Now we can say that the R.H.S. is;

$\frac{cos^2\theta}{sin^2\theta}+1$

Now we add the fraction and get;

$\frac{cos^2\theta+sin^2\theta}{sin^2\theta}$

Now according to trigonometric identity;

$cos^2\theta+sin^2\theta=1$

So, $\frac{cos^2\theta+sin^2\theta}{sin^2\theta}=\frac{1}{sin^2\theta}$

Here,

$csc^2\theta=\frac{1}{sin^2\theta}$ and $Cot^2\theta+1$ = $\frac{1}{sin^2\theta}$ <em> </em>

L.H.S. = R.H.S.

Hence $csc^2\theta=cot^2\theta+1$

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