Mathematics High School


4 Tan A/1-Tan^4=Tan2A + Sin2A​

Answers

Answer 1

tan(2A) + sin(2A) = sin(2A)/cos(2A) + sin(2A)

• rewrite tan = sin/cos

… = 1/cos(2A) (sin(2A) + sin(2A) cos(2A))

• expand the functions of 2A using the double angle identities

… = 2/(2 cos²(A) - 1) (sin(A) cos(A) + sin(A) cos(A) (cos²(A) - sin²(A)))

• factor out sin(A) cos(A)

… = 2 sin(A) cos(A)/(2 cos²(A) - 1) (1 + cos²(A) - sin²(A))

• simplify the last factor using the Pythagorean identity, 1 - sin²(A) = cos²(A)

… = 2 sin(A) cos(A)/(2 cos²(A) - 1) (2 cos²(A))

• rearrange terms in the product

… = 2 sin(A) cos(A) (2 cos²(A))/(2 cos²(A) - 1)

• combine the factors of 2 in the numerator to get 4, and divide through the rightmost product by cos²(A)

… = 4 sin(A) cos(A) / (2 - 1/cos²(A))

• rewrite cos = 1/sec, i.e. sec = 1/cos

… = 4 sin(A) cos(A) / (2 - sec²(A))

• divide through again by cos²(A)

… = (4 sin(A)/cos(A)) / (2/cos²(A) - sec²(A)/cos²(A))

• rewrite sin/cos = tan and 1/cos = sec

… = 4 tan(A) / (2 sec²(A) - sec⁴(A))

• factor out sec²(A) in the denominator

… = 4 tan(A) / (sec²(A) (2 - sec²(A)))

• rewrite using the Pythagorean identity, sec²(A) = 1 + tan²(A)

… = 4 tan(A) / ((1 + tan²(A)) (2 - (1 + tan²(A))))

• simplify

… = 4 tan(A) / ((1 + tan²(A)) (1 - tan²(A)))

• condense the denominator as the difference of squares

… = 4 tan(A) / (1 - tan⁴(A))

(Note that some of these steps are optional or can be done simultaneously)

Related Questions

The yellow turtle country covered 33 cm in six minutes her speed as a unit rate is blank a country walk blank in one minute

Answers

Answer:

5.5 cm/minute

Step-by-step explanation:

Given that,

The yellow turtle country covered 33 cm in six minutes.

To find unit rate, divide distance covered by the time.

Here, distance = 33 cm

Time, t = 6 minutes

[tex]R=\dfrac{33\ \text{cm}}{6\ \text{minutes}}\\\\=5.5\ \text{cm/minutes}[/tex]

Hence, the unit rate is 5.5 cm/minute. It means, Courtney covered 5.5 cm in one minute.

If the temperature outside increases by 3 1/2 degrees every 1 1/2 hours, by how much will the temperature increase after 4 hours?

please answer in fractions.

Part 1:

What is the rate per hour of the temperature increase?

Part 2:

How much will the temperature increase after 4 hours?

Answers

Answer:

Part 1:    7/3 degrees/hour

Part 2:    28/3 degrees

Step-by-step explanation:

Part 1:

3 1/2 degrees per 1 1/2 hours =

= (3 1/2)/(1 1/2)

= (7/2) / (3/2)

= 7/2 * 2/3

= 7/3 degrees/hour

The rate is 7/3 degree per hour

Part 2:

In 4 hours, the temperature goes up 4 times what it goes up in 1 hour.

4 hours * 7/3 degree/hour = 28/3 degrees

50 points!!! If your good at math please help! :) will give brainlest
Y is directly related to X, and Y is 81 when X is 27.

The constant of variation is ___
(there are no answer choices, it's just a type in box so i need an exact answer please! :))

Answers

Answer:

y=3x or x=y/3

Step-by-step explanation:

81, y divided by 3 is equal to 27.

The diagonals of rhombus ABCD intersect at E. Given that m∠CAD=20° and CE=4, find the m∠CDA.

Answers

Given :

The diagonals of rhombus ABCD intersect at E.

∠CAD = 20°.

To Find :

The angle ∠CDA.

Solution :

We know, diagonals of a rhombus bisects each other perpendicularly.

So, ∠DEA = 90°.

In triangle ΔEAD :

∠EAD + ∠AED + ∠EDA = 180°

20° + 90° + ∠EDA = 180°

∠EDA = 70°

Now, we know diagonal of rhombus also bisect the angle between two sides .

So, ∠CDA = 2∠EDA

∠CDA = 2×70°

∠CDA =140°

Therefore, ∠CDA is 140°.

Mikhail has $4.15. If he buys one pack of candy canes, how much money does he have left? (the candy canes are $2.45 FOR A PACK OF 4 candy canes)

Answers

Answer:

1.70$

Step-by-step explanation:

$4.15-$2.45

=1.70$

Answer:

$1.70

Step-by-step explanation:

If you subtract the price of one pack of candy canes from how much money he has you get $1.70

(hope this helps)

. William fills 1/3 of a water bottle in 1/6 of a minute. How much time will it
take him to fill the bottle?

Answers

Answer:

1/2 minute

Step-by-step explanation:

We can use a ratio to solve

1/3 bottle     1 bottle

------------   = --------------

1/6 minute    x minutes

Using cross products

1/3x = 1/6 *1

1/3 x = 1/6

Multiply each side by 3

3 * 1/3x = 3 * 1/6

x = 3/6

x = 1/2

1/2 minute

Answer:

30 seconds (1/2 minute)

Step-by-step explanation:

We are given that,

Amount of water filled in 1/6 minute = 1/3

Now, Let the time taken to fill the whole bottle with water be x

Hence,

Through the ratio method we get,

1/3:1/6 : : 1:x

Hence, we need to multiply the extremes and the means together and equalize them.

Hence,

x/3=1/6

x=(1/6)×3

x=(1/2) minute or 30 seconds

20 POINTS and BRAINLIEST
Solve the simultaneous equation!

Answers

Answer:

x=7 y=-2

Step-by-step explanation:

sin 40 cos 50 + cos 40 sin 50 find the value​

Answers

Answer:

= 1

Step-by-step explanation:

0.4131 + 0.5868 = 0.999 --> 1

The height of a room is 10 feet. You are installing floor-to-ceiling shelving, and each shelf is 8 inches tall. Write and solve an inequality for the number of shelves you could possibly build.

Answers

10 feet = 120 inches

120 divided by 8 = 15

you can have 15 shelves in the room

10ft=120
120 divided by 8=15

integral 1-rootx/x dx​

Answers

r-1 over 2 |d| to2 r2 x3 +C

please help me !!!!!!!!!!!!!!!!

Answers

5Step-by-step explanation:

help me find m and b

Answers

Answer:

m = 2/3

b = -1

y = 2/3x - 1

Step-by-step explanation:

Answer:

y=2/3x-1

Step-by-step explanation:

What is the greatest cornron foctor (Gc) of 15 and 64?

Answers

The GCF of 15 and 64 is 1.

A pair of designer blue jeans is on sale for $51. This is 75% of the original price. What was the original price of the jeans?

Answers

22 hope this helps have a nice day

Find the measure of the indicated angle. Round to the nearest tenth of a
degree.

Answers

Step-by-step explanation:

Using trignometry, we have cosθ = Adjacent / Hypotenuse = 3/5.

Hence θ = cos-1(3/5) = 53.1° (A).

Answer I will mark branliest

Answers

Answer:

D 50

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

5y^2+4x

5(3)^2+4(2.5)

5(9)+4(2.5)

45+4(2.5)

45+10

=55

What will be the distance from the center of dilation, P, to the image S'?

2 units
4 units
6 units
8 units

Answers

Answer:

the answer is 6 units..

You notice a hot air balloon descending. The elevation h (in feet) of the balloon is modeled by the function h(x)=−6x+330, where x is the time (in seconds) since you first noticed the hot air balloon. ANSWER FASTTTTT!!!

Answers

Answer:

55 secs

Step-by-step explanation:

Given the elevation h (in feet) of the balloon modeled by the function h(x)=−6x+330, we can calculate the time it takes the balloon to reach the ground. The hot air balloon hits the ground at h(x) = 0.

Substitute h(x) = 0 into the modeled expression and find x as shown;

h(x)=−6x+330

0 = −6x+330

6x = 330

Divide both sides by 6

6x/6 = 330/6

x = 55 seconds

Hence the hot air balloon hits the ground after 55 seconds

A color printer prints 21 pages in 9 minutes. How many pages does it print per minute? Round your answer to the nearest hundredth.
? = pages per minute

Answers

Answer:

2.33 = x

Step-by-step explanation:

pages minutes

21 9

x 1

Cross multiply.

21×1 = 9×x

21 9x

9 9

9 cancels 9 leaving x. and 21 divided by 9 equals 2.33 pages. NB. both sides are divided by 9 because we want x by itself and what you do to one side, you have to do to the other.

The scores on a test are normally distrubuted with a mean of 60 and a standard deviation of 12. What is the score that is 2 1/2 standard deviations above the mean?

Answers

Answer:

?

Step-by-step explanation:

Question 3 (2 points)
Use the figure below to answer the following questions. Find the measure of each angle.

Answers

Answer:

∠ 1 = 70°, ∠ 2 = 140

Step-by-step explanation:

110° and the adjacent angle inside the triangle are supplementary, then

angle = 180° - 110° = 70°

Since 2 sides of the triangle are congruent, then the triangle is isosceles

Thus the 2 base angles are congruent, then

∠ 1 = 70°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ 2 is an exterior angle of the triangle, thus

∠ 2 = 70° + 70° = 140°

Rosalina is driving to visit her family which live 150 km away her average speed is 60 km/h the cars tank is 20 L of fuel at the beginning of the drive and its fuel efficiency is 6 km perL fuel cost $.60 per liter how long can Roselene drive before she runs out of fuel

Answers

Answer:

With the amount of fuel she has, she can drive 120 km which will take 2 hours.

Step-by-step explanation:

You need to figure out which information is necessary for this problem and which is not.

The fuel tank has 20 L.

The car drives 6 km per L.

20 L * 6 km/L = 120 km

She can drive 120 km with the amount of fuel she has.

She is driving at 60 km/h.

speed = distance/time

time * speed = distance

time = distance/speed

time = (120 km)/(60 km/h) = 2 hours

Answer: With the amount of fuel she has, she can drive 120 km which will take 2 hours.

what fraction is 3/4 equivalent to?

Answers

Answer:

6/8

Step-by-step explanation:

double both of them lol

Answer:

3/4 is equivalent to 6/8 and 12/16

Step-by-step explanation:

Please help me out!!!!!

Answers

Answer:

To find a degree 3 equation you must find and take the roots.You have the roots at x=0 Now plug those into the equation for example: (x-4) would result in x1=4Hope this helps!

PLZ do all of it plz i will give brainlest and thanks to best answer

Answers

Answer:

1. -4

2. 10

3. -19

4. 5

Step-by-step explanation:

1. 5 + -9= -4

2. -3 + 13 = 10

3. -8 + 11 = -19

4. 6 + -1 = 5

Please help me, TYSM !!❣

Answers

Answer:

A

Step-by-step explanation:

thats my best guess, but im not positive sorry if im wrong!

Find the value of x.

Answers

Answer:

x = 78

Step-by-step explanation:

180 - 60 - 42 = 78

Pardon me if i'm wrong :/

You would use Pythagorean theorem to solve. A+B=C

A woman sold a typewriter for Rs 13718 in the system of compound depriciation at the rate of 5 percent .If she had purchased it 3 years before how much did she pay for it by that time?

Answers

Answer:

Rs 16000

Step-by-step explanation:

Given that :

Price at which typewriter was sold = Rs 13718

Compound Depreciation rate = 5%

Time = 3 years

Amount paid for typewriter 3 years ago

Using the relation :

Final amount = Initial amount(1 - r/n)^nt

n = number of compounding times per period

Rate = r = 5% = 0.05

t = time

A = Final amount = 13718

Initial amount = original purchase price (p)

Therefore ;

13718 = p(1 - 0.05)^3

13718 = p(0.95)^3

13718 = p * 0.857375

13718 = 0.857375p

p = 13718 / 0.857375

P = Rs 16000

Amount paid at the time of purchase = 16000

three fourths times two thirds .
a
five twelfths

b
six twelfths

c
five sevenths

d
six sevenths

Answers

Answer: 1/2

Step-by-step explanation: 3/4x2/3= 6/12=3/6=1/2. Hope this helps! Have a wonderful day/night! PLz mark me as brainliest!

Answer:

b) six twelfths

Step-by-step explanation:

(3/4)*(2/3) = 0.50.5 = 1/2 = 6/12 = six twelfths

picture above
give the right answer and i’ll literally give 75 extra points and brainliest x2 , please help i can’t fail

Answers

Answer:

False :)

Step-by-step explanation:

Answer:

Not a function, therefore false.

Step-by-step explanation:

Maybe this attachment can help.

Other Questions
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