Which of these expressions is the simplified form of the expression (StartFraction sine (x) Over 1 minus cosine squared (x) EndFraction) tangent (StartFraction x Over 2 EndFraction) ?
Answers
Given:
[tex]\dfrac{\sin (x)}{1-\cos ^2 (x)}\tan \left(\dfrac{x}{2}\right)[/tex].
To find:
The expression, which is equivalent to the given expression.
Solution:
We have,
[tex]\dfrac{\sin (x)}{1-\cos ^2 (x)}\tan \left(\dfrac{x}{2}\right)[/tex]
[tex]=\dfrac{\sin (x)}{1^2-\cos ^2 (x)}\times \dfrac{1-\cos (x)}{\sin (x)}[/tex] [tex][\because \tan \left(\dfrac{x}{2}\right)=\dfrac{1-\cos (x)}{\sin (x)}][/tex]
[tex]=\dfrac{\sin (x)}{(1-\cos (x))(1+\cos (x))}\times \dfrac{1-\cos (x)}{\sin (x)}[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
Cancel out the common factors.
[tex]=\dfrac{1}{1+\cos (x)}[/tex]
Therefore, the correct option is C.
Given question is incomplete; find the complete question in the attachment.
Simplified form of the given trigonometric expression will be represented by Option C.
Given expression is,
[tex][\frac{\text{sin(x)}}{1-\text{cos}^2(x)}]\tan(\frac{x}{2} )[/tex][tex][\frac{\text{sin(x)}}{1-\text{cos}^2(x)}]\tan(\frac{x}{2} )=\frac{\text{sin(x)}}{1-\text{cos}^2(x)}\times \frac{1-\text{cos}x}{\text{sinx}}[/tex] [Since. [tex]\text{tan}\frac{x}{2} =\frac{1-\text{cosx}}{sinx}[/tex]]
[tex]=\frac{1-\text{cos}x}{(1-\text{cosx})(1+\text{cosx})}[/tex]
[tex]=\frac{1}{1+\text{cosx}}[/tex]
Therefore, Option C will be the correct option.
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Related Questions
PLSS HELPP
What is the value of x in this equation?
4x − 2(2x − 2) = 2(2x − 4)
Answers
2.) Bill sells cleaning products on commission. He earns 40% commission on his sales. If
he has sales of $983, how much commission does he earn?
Answers
Answer:
$393.20
Step-by-step explanation:
There are two easy ways to solve this:
1) Use a setup and cross multiply.
First, set up your problem.
$ x = 40%
$983 100%
$983 is the total amount, so it is equal to 100%. We're trying to find 40% of it, so we can label the amount as $x. Remember, each side has to be in the same type of measurements (i.e. dollars, percentages, inches, etc.).
Then, cross multiply. You should end up with:
100x = 39,320
Then, simplify.
x = 393.2
x = $393.20
2) Convert the percentage to a decimal and multiply.
First, convert the percentage you're looking for into a decimal:
40% × 100 = 0.4
Then, multiply the decimal with the total sales amount:
$983 × 0.4 = 393.2
= $393.20
40% × 100 = 0.4
$983 × 0.4 = $393.20
Bill earns $393.20 commission total.
Jessica, Kareem, and Lamar served a total of 64 orders Monday at the school cafeteria. Jessica served 8 fewer orders than Lamar. Kareem served 2 times as
many orders as Lamar. How many orders did they each serve?
Answers
Answer:
Jessica: 10 orders
Lamar: 18 orders
Kareem: 36 orders
Step-by-step explanation:
Let's first designate each person with a letter.
The number of orders served by Jessica can be designated as [tex]J[/tex]
The number of orders served by Kareem can be designated as [tex]K[/tex]
The number of orders served by Lamar can be designated as [tex]L[/tex]
We know that they all served a total of 64 orders. This can be expressed as the sum of their orders equaling 64.
[tex]J+K+L=64[/tex]
We also know that Jessica served 8 fewer orders than Lamar. This can be expressed as the number of orders served by Jessica, [tex]J[/tex], being equal to Lamar's orders [tex]L[/tex] minus 8.
[tex]J = L-8[/tex]
Fianlly, we know that Kareem served twice as many orders as Lamar. This can be expressed as the number of order's served by Kareem, [tex]K[/tex], being 2 times Lamar's orders [tex]L[/tex].
[tex]K = 2L[/tex]
With these 2 equalities, we can substitute [tex]J[/tex] and [tex]K[/tex] in our original equation,
[tex]J+K+L=64[/tex]
with their values expressed as a subtraction or multiplication of [tex]L[/tex].
[tex]J[/tex] will be substituted with [tex]L-8[/tex], and [tex]K[/tex] will be substituted with [tex]2L[/tex].
[tex]J+K+L=64[/tex]
With substitutions:
[tex](L-8) + 2L + L = 64[/tex]
We can simplify this by combining the L-terms:
[tex]L + 2L + L -8 = 64\\4L - 8 = 64[/tex]
Next, we'll add 8 to both sides.
[tex]4L = 72[/tex]
Divide both sides by 4:
[tex]L = 18[/tex]
Thus, Lamar served 18 orders.
Using our expressions, we can find how many orders the others served.
Jessica:
[tex]J = L-8\\J = 18 -8\\J = 10[/tex]
Jessica served 10 orders.
Kareem:
[tex]K = 2L\\K = 2*18\\K = 36[/tex]
Kareem served 36 orders.
Using the diagram, determine whether the angles are vertical angles, a linear pair, or neither. (Image is included)
Answers
Answer:
1.linear pair
2. neither
3. vertical
4. neither
5. vertical
6. neither
7. linear pair
8. neither
Step-by-step explanation:
the answers are starting from up to down, not side to side
We have the definitions of the Adjacent angles, linear angles, vertical angles.
Two angles are considered to be adjacent angles when they share a common vertex, a common side, but no common interior pointsWhen two lines intersect each other at a single point, linear pair of angles are formed. If the angles so formed are adjacent to each other after the intersection of the two lines, the angles are said to be linear.Two angles are said to be vertical angles when their sides form two pairs of opposite rays (straight lines).So, from the figure we see that
<1 and <2 are linear pair <2 and <4 are neither <6 and <8 are vertical <11 and <1 are neither<1 and <3 are vertical <4 and <5 are neither <8 and <9 are linear pair <10 and <7 are neitherLearn more:https://brainly.com/question/3182415
Evaluate the following: −3 − (−8).
Answers
Answer:
5
Step-by-step explanation:
When you have a negative next to a negative, you can turn it into a positive. For example the -(-8) would now be +8. This is called the airplane strategy because it forms a airplane if you flip you sheet of paper or your device.
From here, we have -3+8.
Now we subtract since each value has a different sign and we get +5.
Hope this helps!! :)
Answer:
5
Step-by-step explanation:
-*-=+
-*+=-
+*+=+
-3-(-8)=5
-3+8=5
MARKING BRAINLY PLEASE JUST HELPPP
Planet Earth has a mass of 5.9726 × 10 24 kilograms. And although 70% of the Earth's surface is made of water, the water's mass is only 5 × 10 -4 percent of the Earth's total mass. Use scientific notation to estimate the mass of the planet's water. In your final answer, include all of your estimates and calculations.
Answers
Answer:
i don't it is correct or not........
Step-by-step explanation:
The Mass of Earth = 5.9742 × 1024 kilograms == == The Earth is (As of May 2000) is thought to be approximately 5.972 sextillion (5,972,000,000,000,000,000,000) metric tons.
A metric ton is a thousand kilograms, or 2,204.62 pounds.
Approximately 6,000,000,000,000,000,000,000,000 (6x1024) kilograms.
Answer:
Mass on water on earth is 29.5×10^20 kg approximately.
Step-by-step explanation:
Mass of earth= 5.9726 × 10^ 24 kg
water's mass is only 5 × 10 -4 percent of the Earth's total mass.
so mass of water = 5.9726×10^24 kg×5×10^-4=29.8603×10^20kg approximately
Question 11 of 17
What division equation does the model show ?
Answers
Will Give brainliest plus 25 points
Answers
Psychology 101: Is it normal for school age people to have crushes on their teachers or professors?
Answers
Answer:
it is normal, but not right to act upon
Solve for x. 4(x+1)= -3x-10
Answers
Answer:
4x+4=-3x-10
4x+3x=-10-4
x= -14
Step-by-step explanation:
Answer:
x = -2
Step-by-step explanation:
P.E.M.D.A.S
4(x + 1) = 4x+4
now we have 4x + 4 = -3x - 10.
now we can combine like terms which are x
4x and -3x, to combine like terms we can either subtract 4x on both sides or -3x on both sides, but lets do 4x.
now we have this
4x + 4 = -3x - 10.
-4x -4x
= 4 = -7x - 10
now we can isolate x by its self so we have to add 10 on both sides
4 = -7x - 10
+10 +10
and we get
14 = -7x
now we can divide -7 to get x by its self
14/-7 = -7/x
we get for our final answer
x = -2
what is six less than 9
Answers
Answer:
3
Step-by-step explanation:
9-6=3
The merry-go-round at the fair rotates 12 times each minute, and children are 15 feet from the center of the wheel when they are in their seats. What is the linear velocity of the children in feet per hour?
360π
720π
21,600π
43,200π
Answers
Answer:
i think c 21600pi
Step-by-step explanation:
Answer:
C. 21600π
Step-by-step explanation:
Compute please help
Answers
Answer:
- 3.46 + ( - 4.23 ) = 7.69
- 5.6 + 27.4 = 21.8
Simplify: (x3 y-2)12 (x-5y)-12
A) xy
B) x12xy
C) yx
D) y12xy
Answers
Answer: b
Step-by-step explanation:
. Steve drove for 812 hours at 72 miles per hour. How much distance did he travel?
Answers
Answer:
58464
Step-by-step explanation:
Multiply the two numbers
Answer:
If Steve drives for 812 hours at 72 miles per hour, he drives 58,464 miles in total.(Side Note: if you mean 8 1/2 hours then it's 612 miles
Step-by-step explanation:
To find distance dealing with time and speed, we can use the formula d=rt.
D= Distance
R= Speed
T= Time
Now we plug in our values! D=72 × 812 and we get D= 58,464 miles or if you meant 8 1/2 hours, then it's 612 miles
Hope this helps! :)
what’s 4 2/3 divided by 3 1/2 ?
Answers
Answer:
the answer to this problemis 1 1/3
Can you conclude with a high degree of confidence that the population means for Iowa and New Jersey students are different? A. Because of the extremely low p-value, we cannot reject the null hypothesis with a very high degree of confidence. Hence, the population means for Iowa and New Jersey students are not different. B. Because of the extremely high p-value, we can reject the null hypothesis with a very high degree of confidence. Hence, the population means for Iowa and New Jersey students are different. C. Because of the extremely low p-value, we can reject the null hypothesis with a very high degree of confidence. Hence, the population means for Iowa and New Jersey students are different. D. Because of the extremely high p-value, we cannot reject the null hypothesis with a very high degree of confidence. Hence, the population means for Iowa and New Jersey students are not different.
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
Option A is correct
Step-by-step explanation:
From the question we are told that
The 95% confidence interval of the mean score of all New Jersey third graders is (58.957 , 63.043)
The sample size is n = 184
The sample average is [tex]\mu = 65 \ points[/tex]
The standard deviation is [tex]\sigma = 13 \ points[/tex]
The 90% confidence interval for the difference in mean score between lowa and New Jersey is (-6.33 , -1.67 )
The p-value is [tex]p-value = 0.0048[/tex]
Generally given that the p-values is very low compared to the level of significance (100 -90 = 10% = 0.10 ) we can reject the null hypothesis which is usually a claim that the means of the population are the same )
Hence the population means are different .
A corporate team-building event costs $4 for every attendee. How many attendees can
there be, at most, if the budget for the corporate team-building event is $36?
Answers
Someone please help me.
Answers
Answer:
C
Step-by-step explanation:
Prime factors: 2, 3, 3
wolverine and cyclops ordered large pizzas for dinner. Wolverine ate 1-3/8 pizzas and cyclops ate 1/12 of a pizza. which of the following statements is true
Answers
Answer:
What statements are you talking about
Step-by-step explanation:
What is the fraction in simplest form?
14/16
7/8
28/32
7/16
7/9
Answers
Answer:
7/8
Step-by-step explanation:
factorizar por el motodo de aspas
[tex]12x^2 = 3x + 2[/tex]
Answers
Answer:
Step-by-step explanation:
12x²-3x=2
[tex]x^2-\frac{1}{4}x=\frac{1}{6}\\x^2-\frac{1}{4}x+\frac{1}{64}=\frac{1}{6}+\frac{1}{64}\\(x-\frac{1}{8})^2=\frac{ 32+3 }{192}=\frac{35}{192}\\\\(x-\frac{1}{8} )^2-(\sqrt{\frac{35}{192} } )^2=0\\(x-\frac{1}{8} +\sqrt{\frac{35}{192} } )(x-\frac{1}{8} -\sqrt{\frac{35}{192} } )=0[/tex]
I have a six sided cube what is the experimental probability of rolling a six
Answers
help ASAP. Which relation is a function?
Answers
Answer:
Top right graph.
Step-by-step explanation:
In order for a graph to be a function, it must pass the Vertical Line Test. All the graphs fail to pass the Vertical Line Test except for the top right graph.
Each x-value must have only 1 y-value. No 1 x-value can hold 2 y-values.
A cereal box is 8 inches by 2 inches by 12 inches. What is its surface area?
Answers
Answer:
272 inches squared
Step-by-step explanation:
272 square inches.
Because (2×8×2) + (2×8×12) + (2×2×12) = 32 + 192 + 48 = 272
In Mr.Vargas 7th periodClass 12 out of 32 students received a failing grade what is the percentage of the students who passed
Answers
Answer: 20
Step-by-step explanation:
Answer:
20
Step-by-step explanation:32-12=20
20+12=32
Javier has a basket of oranges and apples. The number of oranges is 2 more than twice the number of apples in the basket. The difference of half the number of oranges and half the number of apples is 4.
An equation created to find the number of apples Javier has in the basket will have
Answers
Number of oranges is (2a + 2)
Half the number of oranges is 1/2(2a + 2)
Half the number of apples is 1/2a
The difference between half the number of oranges and half the number of apples equals 4 looks like this:
1/2(2a + 2) - 1/2a = 4
Now solve.
1/2(2a + 2) - 1/2a = 4 (multiply 1/2 by what's inside the parenthesis)
1a + 1 - 1/2a = 4
1a + 1 -1 - 1/2a = 4 - 1
1a - 1/2a = 3
1/2a = 3
1/2a ÷ 1/2 = 3 ÷ 1/2
a = 6
He has 6 apples.
Substitute 6 into the equation for the number of oranges.
2a + 2
2(6) + 2 = 14
He has 14 oranges.
Check your work.
The difference between half the number of oranges (7) and half the number of apples (3) does indeed equal 4.
Therefore, the equation has one solution.
Answer:
it is one solutionStep-by-step explanation:
what is the slope of -1,3 and 3,15
Answers
Answer:
3
Step-by-step explanation:
whats 8.546 rounded to the nearest one
Answers
Answer:
9
Step-by-step explanation:
ok so first if the place you're rounding to is 5 or more you round up and if the place is 4 or less then it stays the same
8.5
5 is 5 or more so you round up
to 9
x times y equals 45.
What is x and y?
Answers
Answer:
9 and 5
Step-by-step explanation:
There are many answers
Answer:
There could be a different answer but this is what i got.
Step-by-step explanation:
1 x 45,
3 x 15,
or 5 x 9