1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
rewona [7]
3 years ago
7

Solve the following equation on the interval [0, 2π). tan^2x sin x = tan^2x

Mathematics
1 answer:
Alenkasestr [34]3 years ago
8 0
<h3>Given</h3>

tan(x)²·sin(x) = tan(x)²

<h3>Find</h3>

x on the interval [0, 2π)

<h3>Solution</h3>

Subtract the right side and factor. Then make use of the zero-product rule.

... tan(x)²·sin(x) -tan(x)² = 0

... tan(x)²·(sin(x) -1) = 0

This is an indeterminate form at x = π/2 and undefined at x = 3π/2. We can resolve the indeterminate form by using an identity for tan(x)²:

... tan(x)² = sin(x)²/cos(x)² = sin(x)²/(1 -sin(x)²)

Then our equation becomes

... sin(x)²·(sin(x) -1)/((1 -sin(x))(1 +sin(x))) = 0

... -sin(x)²/(1 +sin(x)) = 0

Now, we know the only solutions are found where sin(x) = 0, at ...

... x ∈ {0, π}

You might be interested in
I've done everything I can, I cant figure this out pls help asap
sergeinik [125]

1. H

2. A

3. E

4. C

I have to type extra words to turn this in so basically I just found the slop of the line then matched it with the letters...

7 0
2 years ago
Ricardo is constructing a line through point P that is perpendicular to line m. He has already constructed the arc shown.
gogolik [260]
I took this test and got 100% it is #4 :)
3 0
3 years ago
Read 2 more answers
Bethany has 43 apples.write a subtraction story about the apples that would require regrouping.
RoseWind [281]
Hey there!

21 apples were rotten and got thrown out. The remaining apples were divided equally among 11 people
8 0
2 years ago
Read 2 more answers
Help me pls! I’ll give u 15 points!
kykrilka [37]

Answer:

add 15 by 19 by 12 to get 46 than cut it in half to get 23!

Hope i helped please mark brainiest I need it!

6 0
3 years ago
What is the slope of the line shown in the graph? (4 points)<br> 5<br> 4<br> 1<br> 0<br> 10
Softa [21]

Answer:

There is no graph

Step-by-step explanation:

Post the graph and I can help you.

6 0
3 years ago
Other questions:
  • Complete the square<br> x2 - 6x +____<br> 7 = -13+____
    11·2 answers
  • The heights, in inches, of several seventh-grade students at Evan Mills Middle School are listed below.
    5·1 answer
  • Which of the following names apply to this number? 2
    10·1 answer
  • Annie is sledding down a snow-covered hill. She knows that the steeper the hill, the faster her sled will go.A. The amount of sn
    8·2 answers
  • Anyone have the answer to number 6
    14·2 answers
  • Use the drawing tools to form the correct answer on the grid.
    9·1 answer
  • If you answer right ill give you brainlyist
    15·2 answers
  • Solve the following equation for y. Y= 2y+4y-3=27
    8·1 answer
  • Please help! I will mark as brainliest. &lt;3
    7·2 answers
  • 8 x 10*-3
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!