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3 years ago

In the following diagram, points C, A, and B are collinear. Use complete sentences to describe the sum of and .

Mathematics

2 answers:

pochemuha3 years ago

8 0

Answer:

The sum is CB.

Step-by-step explanation:

This is because of points C, A, and B are all collinear, which means that they all fall on the same line. Since the points are collinear, the sum of CA and AB is the whole line, which is CB. I really hope this helps :)

Maru [420]3 years ago

5 0

The sum of angles CAD and DAB is 180 degrees. This is because they are all on a straight line (because points CAB are colinear) and angles on a straight line add up to 180 degrees.

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Help! How would I solve this trig identity?

NeTakaya

Using simpler trigonometric identities, the given identity was proven below.

<h3>How to solve the trigonometric identity?</h3>

Remember that:

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

Then the identity can be rewritten as:

$sec^4(x) - sen^2(x) = tan^4(x) + tan^2(x)\\\\\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)} = \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)} \\\\$

Now we can multiply both sides by cos⁴(x) to get:

$\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)} = \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)} \\\\\\\\cos^4(x)*(\frac{1}{cos^4(x)} - \frac{1}{cos^2(x)}) = cos^4(x)*( \frac{sin^4(x)}{cos^4(x)} + \frac{sin^2(x)}{cos^2(x)})\\\\1 - cos^2(x) = sin^4(x) + cos^2(x)*sin^2(x)\\\\1 - cos^2(x) = sin^2(x)*sin^2(x) + cos^2(x)*sin^2(x)$

Now we can use the identity:

sin²(x) + cos²(x) = 1

$1 - cos^2(x) = sin^2(x)*(sin^2(x) + cos^2(x)) = sin^2(x)\\\\1 = sin^2(x) + cos^2(x) = 1$

Thus, the identity was proven.

If you want to learn more about trigonometric identities:

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hichkok12 [17]

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Step-by-step explanation:

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emmasim [6.3K]

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Fynjy0 [20]

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