Answers
x = 0
Simplify — x/ 2
x ((((cs•(c2))•x)-2c3sx2ot)+((co•(t2))•x))-((ta•(n2))•—) = 0 2
xtan2 ((((cs•(c2))•x)-2c3sx2ot)+((co•(t2))•x))
Equivalent Fraction:
Rewrite the whole as a fraction using 2 as the denominator :
-2c3sx2ot + c3sx + cxot2 (-2c3sx2ot + c3sx + cxot2) • 2 -2c3sx2ot + c3sx + cxot2 = 0
The equations are solved below using trigonometric identities.
What are trigonometric identities?Trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined.
[tex]\frac{sin(x)}{1-cos(x)} -cot(x) = cosec(x) \\\\LHS= \\\\=\frac{sin(x)}{1-cos(x)} -cot(x) \\\\=\frac{sin(x)}{1-cos(x)} -\frac{cos(x)}{sin(x)}\\ \\\frac{sin^{2}(x) - (1-cos(x))cos(x) }{sin(x)(1-cos(x))}\\\\=\frac{sin^{2}(x)-cos(x) +cos^{2}(x) }{sin(x)(1-cos(x))}\\\\=\frac{1-cos(x)}{sin(x)(1-cos(x))}\\ \\=\frac{1}{sin(x)} \\\\=cosec(x)\\\\RHS=\\\\=cosec(x)[/tex]
[tex]cosec(x)^{2} - 2cosec(x)cot(x) + cot(x)^{2} = tan^{2}(\frac{x}{2})\\\\LHS= \\\\= cosec(x)^{2} - 2cosec(x)cot(x) + cot(x)^{2} \\\\=( cosec(x) - cot(x) )^{2} \\\\=(\frac{1-cos(x)}{sin(x)}) ^{2}\\\\=(\frac{(1-cos(x))(1+cos(x))}{sin(x)(1+cos(x))}) ^{2}\\\\=(\frac{sin(x)^{2} }{sin(x)(1+cos(x))}) ^{2}\\\\=(\frac{sin(x) }{1+cos(x)}) ^{2}\\\\=(\frac{2sin(x/2)cos(x/2) }{1+2cos^{2}(x/2)-1}) ^{2}\\\\= (\frac{sin(x/2)cos(x/2) }{cos^{2}(x/2)}) ^{2}\\\\= tan^{2}\frac{x}{2}\\\\RHS = \\\\=tan^{2}\frac{x}{2}[/tex]
Learn more about trigonometric identities here
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Related Questions
The product of 18 and Q algebra expression
Answers
Answer:
18q
Step-by-step explanation:
18*q=18q
Hope that helped :)
Answer:
[tex]18 \times q[/tex]
[tex]18q[/tex]
multiply 18 by q to get 18q as the answer
how much are 3 books if they add up to $24 and all of the prices are multiples of 4
Answers
Find the measure of each marked angle.
Answers
Answer:
X= 15, m∠78°
Step-by-step explanation:
Since the angles are vertically opposite
Therefore their measurements are equal
Therefore (2x + 48 ) = (5x + 3 )
So,
[tex](2x + 48) = (5x + 3)\\(2x-5x)= (3-48)\\-3x = -45\\x = -45/-3\\x = 15[/tex]
[tex](2x + 48)\\=( 2* 15 + 48)\\= 30 + 48\\=78\\\\(5x + 3)\\=(5*15 + 3)\\=75+3\\=78[/tex]
They both equal 78°
From an elevation of 0.5 m below the surface of the water, a swimmer dives at a rate of 0.25 m/s. What is the depth of the swimmer after 4 minutes?
Answers
Answer:
gg
Step-by-step explanation:
Solve for x
And show work
Answers
Answer:
2x - 20 + 7 = x - 1
2x - 13 = x-1
2x = x+12
x = 12
The formula for the volume of a cone is shown below. V represents the volume, r radius and h height.
What is the height of a cone with a volume of 110 cubic cm and a base of 5 cm (so the radius is 2.5 cm)
V=1/3pir^2h
Answers
Answer:
110/5=2
2,5.5=15
2+15=17
Step-by-step explanation:
help me with this problem please
Answers
Answer:
[tex]y = \frac{ - 3x + 6}{2} = \\ x = 4 \\ y = \frac{ - 3 \times 4 + 6}{2} = \frac{ - 12 + 6}{2} = \frac{ - 6}{2} = - 3[/tex]
How do you graph 2x+5
Answers
Answer:
Read explanation
Step-by-step explanation:
First you put a point on (0,5). Then you perform rise/run which is the slope. The slope is 2. So from (0,5) you go up 2 and to the right one and make another point. You then use a ruler and draw a line connecting them and put arrows at the end.
2x + y + 6z = + 1
3x + 2y + 5z = 16
7x + 3y - 4z = 11
Answers
Answer:
1) x=1/2-y/2-3z
2)x= 16/3- 2y/3- 5z/3
3)x= 11/7- 3y/7+ 4z/7
Step-by-step explanation:
isolate the variable, to do that divide each side by the factors that don't contain the variable
If f(x) is an exponential function where f(-2) = 1 and f(7) = 63, then find the
value of f(1), to the nearest hundredth.
Answers
An exponential function is represented as: [tex]\mathbf{f(x) = ab^x}[/tex]
The value of f(1) is 3.95
f(-2) = 1 means that:
[tex]\mathbf{ab^{-2} = 1}[/tex]
f(7) = 63 means that:
[tex]\mathbf{ab^{7} = 63}[/tex]
Divide both equations
[tex]\mathbf{\frac{ab^7}{ab^{-2}} = \frac{63}{1}}[/tex]
Apply law of indices
[tex]\mathbf{b^9 = 63}[/tex]
Take 9th root of both sides
[tex]\mathbf{b =1.58}[/tex]
Make a, the subject in [tex]\mathbf{ab^{-2} = 1}[/tex]
[tex]\mathbf{a = \frac{1}{b^{-2}}}[/tex]
[tex]\mathbf{a = b^2}[/tex]
Substitute [tex]\mathbf{b =1.58}[/tex]
[tex]\mathbf{a = 1.58^2}[/tex]
[tex]\mathbf{a = 2.50}[/tex]
So, we have:
[tex]\mathbf{f(x) = ab^x}[/tex]
[tex]\mathbf{f(x) = 2.50 \times 1.58^x}[/tex]
Substitute 1 for x
[tex]\mathbf{f(1) = 2.50 \times 1.58^1}[/tex]
[tex]\mathbf{f(1) = 3.95}[/tex]
Hence, the value of f(1) is 3.95
Read more about exponential functions at:
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Factor the following
1. 15x+ 20
2. 18x-12
3. 6m+8n+4
Answers
2. 6 (3x -2)
3. 2 (3m + 4n + 2)
5X-50+2X+80-X=180..............
Answers
Hey there!
5x - 50 + 2x + 80 - x = 180
COMBINE the LIKE TERMS
= 6x + 30 = 180
SUBTRACT 30 to BOTH SIDES
6x + 30 - 30 = 180 - 30
CANCEL out: -30 - 30 because that gives you 0
KEEP: 180 - 30 because it helps solve for the x-value
6x = 180 - 30
180 - 30 = 150
NEW EQUATION: 6x = 150
DIVIDE 6 to BOTH SIDES
6x/6 P 150/6
CANCEL out: 150/6 because that gives you the result of the x-value
x = 150/6
SIMPLIFY IT!
x = 25
Therefore, your answer is: x = 25
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Hope this helps :)
1) Delectable Cookie Company sells chocolate chip cookies for $6.95 per pound and
white chocolate cookies for $5.95 per pound. How many pounds of chocolate chip
cookies should be mixed with 4 pounds of white chocolate cookies to obtain a mixture
that sells for $6.75 per pound?
Answers
Answer: 16lbs
Step-by-step explanation: CCC=Chocolate Chip Cookie; WCC=White Chocolate Cookie.
Set up a table showing the pricing ($/lb) and pounds (lbs) for both cookies. The total value of the WCC is $23.8 ($5.95/lb x 4 lbs). The value of the CCC is 6.95x, where x is the lbs CCC.
CCC WCC
6.95 5.95 $/lb
x 4 lbs
6.95x 23.8 $ Total value [$/lb * lbs]
We want x lbs of CCC cookies such that the total value of cookies divided by the total number of lbs is equal to $6.75/lb. That can be written as:
(6.95x + 5.95*4)/(x+4) = 6.75 [Total value of cookies divided by total weight equals $6.75]
(6.95x + 23.8)/(x+4) = 6.75
6.95x + 23.8 =6.75x + 27
0.2x = 3.2
x = 16 lbs
We need 16 lbs of CCC added to the 4 lbs of WCC for a total weight of 20 lbs and a price of $6.75/lb.
Please help me find the answer.
Answers
Answer: sqrt 91
Step-by-step explanation:
We can substitute in y here as 30, so that 60+102=2x^2
182=2x^2
In the order of operations, it states that exponents comes before multiplication
91=x^2
So x will be the square root of 91
lcm of 120,5200 and 40
Answers
help o don’t know any of theses answers please help me
Answers
Answer:
it's c
Step-by-step explanation:
c is the answer becuse its showing u that ob is perpenlicular to Ac
There are 20 passengers in 10 cars. How many passengers per car?
Answers
Answer:
2 in each car. Simple.
Step-by-step explanation:
Answer: it’s two cause 20 divided by 10 is 2.
PLS HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
5 packages of water and 3 packages of cheese sticks
Step-by-step explanation:
the least common multiple of 6 and 10 is 30
Four students are playing a card game. They decide to choose the first person to play by each selecting a card from the 52-card deck and looking for the highest card in value and suit. They rank the suits from lowest to highest: clubs, diamonds, hearts, and spades. (a) If the card is replaced in the deck after each student chooses, how many possible configurations of the four choices are possible
Answers
Answer:
Step-by-step explanation:
83% of408 ndjfjjfjfjfjfjfjfjfjfjfjfjfnfnnfndndnd
Answers
Answer:
338.64
Step-by-step explanation:
Multiply 408 by .83 and get 338.64.
What does angle A equal
Answers
SinA = 4/6
Take the inverse sin (sin^-1) on the calculator with 4/6. 41.8 degrees should be correct.
A nursery has $50,000 of inventory in dogwood trees and red maple trees. The profit on a dogwood tree is 27% and the profit on a red maple tree is 17%. The profit for the entire stock is 20% how much was invested in each type of tree. I NEED THE ANSWER ASAP PLEASE
Answers
Answer:
Sorry do not have your answer
Step-by-step explanation:
(3n-4n+1)-(8n-4n+17)
Answers
Answer:
-5n - 16
Step-by-step explanation:
Step 1: Distribute the negative sign.
[tex]3n - 4n + 1 + (-1)(8n) + (-1)(-4n) + (-1)(17)[/tex] [tex]3n - 4n + 1 - 8n +4n - 17[/tex]Step 2: Combine like terms.
[tex](3n-4n-8n+4n)+(1-17)[/tex] [tex]-5n - 16[/tex]Therefore, the answer is -5n - 16.
please help me, please
Answers
Answer:
A: 51
B:45
C:29
D:-316
Answer:
a. 51
b. 9
c. -3
d. -316
A package of 5 pairs of insulated gloves costs $38.45 What is the unit price of the pairs of gloves? pls answer fast!!!!
Answers
Answer:
7.69 per gloves
Step-by-step explanation:
solve the equation and check the solution 3x+2(x+2)=22-3(2x-5)
Answers
Answer:
x=3
Step-by-step explanation:
QUICKKK QUICCKK QUICKK PLZZZ HELPP ME
Answers
plsss someone help mee asap. Giving brainliest!!
Answers
Answer:
12.2
the answer is 12.2
using the check method
you will know I am correct
What is the slope of the line that passes through (-8, 12) and (4, 3)?
Answers
(3-12)/(4+8)
Answer -3/4
The base of a triangle is 4x+6cm,the height is 5cm. What is the actual length of the base