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Marina86 [1]
3 years ago
14

Cot^2x csc^2x + 2 csc^2x –cot^2 = 2

Mathematics
1 answer:
kow [346]3 years ago
4 0

Answer:

x = π/2 + πk

Step-by-step explanation:

cot² x csc² x + 2 csc² x − cot² x = 2

Multiply both sides by sin² x:

cot² x + 2 − cos² x = 2 sin² x

Add cos² x to both sides:

cot² x + 2 = 2 sin² x + cos² x

Pythagorean identity:

cot² x + 2 = sin² x + 1

Subtract 1 from both sides:

cot² x + 1 = sin² x

Pythagorean identity:

csc² x = sin² x

Multiply both sides by sin² x:

1 = sin⁴ x

Take the fourth root:

sin x = ±1

Solve for x:

x = π/2 + 2πk, 3π/2 + 2πk

Which simplifies to:

x = π/2 + πk

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How many solutions does the equation 9x-3(x+8)=6x-24
Marina86 [1]
Simplifying
9x + -3(x + 8) = 6x + -24

Reorder the terms:
9x + -3(8 + x) = 6x + -24
9x + (8 * -3 + x * -3) = 6x + -24
9x + (-24 + -3x) = 6x + -24

Reorder the terms:
-24 + 9x + -3x = 6x + -24

Combine like terms: 9x + -3x = 6x
-24 + 6x = 6x + -24

Reorder the terms:
-24 + 6x = -24 + 6x

Add '24' to each side of the equation.
-24 + 24 + 6x = -24 + 24 + 6x

Combine like terms: -24 + 24 = 0
0 + 6x = -24 + 24 + 6x
6x = -24 + 24 + 6x

Combine like terms: -24 + 24 = 0
6x = 0 + 6x
6x = 6x

Add '-6x' to each side of the equation.
6x + -6x = 6x + -6x

Combine like terms: 6x + -6x = 0
0 = 6x + -6x

Combine like terms: 6x + -6x = 0
0 = 0

Solving
0 = 0
7 0
3 years ago
Read 2 more answers
Find the slope between the following points: (-5,2) and (3,9)
Kay [80]

Answer:

M=7/8

Step-by-step explanation:

The equation used to solve this is yz-y1/x2-x1.

This applied to the problem would look like 9-2/3--5

Simplified this would be, 7/8 as your slope

4 0
3 years ago
Daphane gave away 3 more than half of her apples. she gave away 17 apples in all. how many apples did daphne have originally?
inn [45]
Well 17-3 gets you 14 which would be half of her apples. 14x2=28 therefore, Daphne originally had 28 apples. She gave away 17 which means she kept 11 for herself
6 0
3 years ago
HELP FAST!!!<br><br> Find 78% of 380. Round to the nearest tenth if necessary.
bonufazy [111]
78% = 78 / 100 = 0.78

What is 78% of 380

= 78% * 380

= 0.78 * 380

= 296.4

U said I should round it up IF NECESSARY so yeah....


5 0
3 years ago
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Raychel drove to the mountains last week there was heavy traffic on the way there and on the trip took 12 hours when Raychel dro
nevsk [136]
Suppose that this person drives at r mph going to the mountains, and gets there in 12 hours.  Returning, this person drives at (r+20) mph and gets home in 8 hours.  We don't know the distance yet, but can solve for the initial speed, r, by setting

d = 12r = (r+20)(8).  Solving for r, r=40 mph (going) and (40+20)mph = 60 mph (returning.  Since d=12 r, d = (12 hrs)(40 mph) = 480 miles (answer).
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3 years ago
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