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2 years ago

9

Explain how you can use multiplication to find the quotient 3/5 divided by 3/15. Then evaluate the expression

1 answer:

sveta [45]2 years ago

3 0

when you divide 2 fractions, you reverse the second fraction then use multiplication

3/5 divided by 3/15 becomes

3/5 x 15/3 = 45/15 = 3

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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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7 0

1 year ago

You walk 30 m to the north, then turn 90 degrees to your left and walk another 80 m. How far are you from where you originally s

insens350 [35]

You are 110 m away from where you originally started

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2 years ago

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The largest prime factor of twelve is _____. user: identify the fractions as proper, improper, or mixed; however, if the fractio

andrew-mc [135]

The prime factors of 12 are : 2 x 2 x 3.....and 3 is the largest

4 1/3 is a mixed number because it has a whole number and a fraction.

6 0

2 years ago

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Question number 2 answer asap please<br><br><br>

slava [35]

Answer:

The ordered pair that is the solution to the system lies in Quadrant IV

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8 0

2 years ago

find the value of x if A, B and C are collinear points and B is between A and C. AB= 6x, BC= x-5, AC= 23

Irina18 [472]

Answer:

x=4

Step-by-step explanation:

AB + BC = AC

AB= 6x, BC= x-5, AC= 23

Substituting what we know

6x + x-5 = 23

Combine like terms

7x -5 = 23

Add 5 to each side

7x-5+5 =23+5

7x = 28

Divide each side by 7

7x/7 = 28/7

x=4

7 0

2 years ago