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
jenyasd209 [6]
3 years ago
8

Prove whether the following are identities 2tanh 1/2x / 1−tanh^2 1/2 x = sinh x​

Mathematics
1 answer:
Tanzania [10]3 years ago
4 0

Recall that

\cosh^2(x) - \sinh^2(x) = 1

Dividing both sides by cosh²(x) gives

1 - \tanh^2(x) = \mathrm{sech}^2(x)

Also, recall the identity

\sinh(2x) = 2\sinh(x)\cosh(x)

Then

\dfrac{2\tanh\left(\frac x2\right)}{1 - \tanh^2\left(\frac x2\right)} = \dfrac{2\tanh\left(\frac x2\right)}{\mathrm{sech}^2\left(\frac x2\right)} \\\\ \dfrac{2\tanh\left(\frac x2\right)}{1 - \tanh^2\left(\frac x2\right)} = 2\tanh\left(\dfrac x2\right)\cosh^2\left(\dfrac x2\right) \\\\ \dfrac{2\tanh\left(\frac x2\right)}{1 - \tanh^2\left(\frac x2\right)} = 2\sinh\left(\dfrac x2\right)\cosh\left(\dfrac x2\right) \\\\\dfrac{2\tanh\left(\frac x2\right)}{1 - \tanh^2\left(\frac x2\right)} = \sinh(x)

You might be interested in
Factor 24−15 using the GCF.
Maru [420]

Answer:

3

Step-by-step explanation:

<u>3</u>,6,9,12,15,18,21,<u><em>24</em></u>

<u>3</u>,6,9,12,<em><u>15,</u></em>18,21,24

5 0
3 years ago
A volleyball team won 90% of 80 games played.how many games did they win?
andreyandreev [35.5K]

Answer:

72 games won

Step-by-step explanation:

4 0
2 years ago
Aaron is making a jewelry box of wood in the shape of a rectangular prism the jewelry box will have the dimensions shown in the
Natali [406]

Answer:

b. $342

Step-by-step explanation:

Base = Length * width

Base Area = 12 * 5

B = 180 square inches.

Perimeter of the prism will be :

P = 2 (length) + 2 (15)

P = 2 * 12 + 30

P = 54 inches

Height of the jewelry container will be :

X = Ph + 2B

X = 54 * 6 + 2 * 180

X = 684 square inches.

Total cost for paint of jewelry box is :

X * cost per inch

Total cost = 682 * $0.50

Total Cost = $342.

8 0
3 years ago
The probability of a certain event occurring is 0.27. What is the probability that the event will NOT occur?
gulaghasi [49]
<span>The probability of the event that will not occur is 0.73.

</span>
8 0
3 years ago
Read 2 more answers
The terminal sides of 60º angle and 240º angle lie on the same line. True False
DerKrebs [107]
The answer is true..
8 0
3 years ago
Read 2 more answers
Other questions:
  • If the number of bacteria in a colony doubles every 400 hours and there is currently a population of 500 bacteria, what will the
    11·1 answer
  • What is the estimate of 206,834 and 194,268
    5·1 answer
  • » A cylinder has a height of 13 millimeters and a radius of 11 millimeters. What is its
    15·2 answers
  • Rounded to the nearest ten thounsend
    9·1 answer
  • Determine the domain and range. Please help!!
    12·1 answer
  • Which of the following is a rational number?​
    15·1 answer
  • I need help ASAP. Will give 20 points :0 It may look easy, but it's really hard for me
    15·2 answers
  • Please help<br> Find the arc length of the semicircle below
    6·2 answers
  • PLEASE HELP MEEE !!!! ITS GEOMETRY
    13·1 answer
  • Combine Like Terms:<br> 2x + 3 - 5x + 8x + 3x2 + 2<br><br><br><br> Help please
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!