Review the steps in the derivation of the tangent sum identity. The steps are not in order.
A 2-column table with 4 rows. Column 1 has entries 1, 2, 3, 4. Column 2 has entries StartFraction sine (x + y) Over cosine (x + y) EndFraction, StartStartFraction StartFraction sine (x) cosine (y) Over cosine (x) cosine (y) EndFraction + StartFraction cosine (x) sine (y) Over cosine (x) cosine (y) EndFraction OverOver StartFraction cosine (x) cosine (y) Over cosine (x) cosine (y) EndFraction minus StartFraction sine (x) sine (y) Over cosine (x) cosine (y) EndFraction EndEndFraction, StartFraction tangent (x) + tangent (y) Over 1 minus tangent (x) tangent (y) EndFraction, StartFraction sine (X) cosine (y) + cosine (x) sine (y) Over cosine (x) cosine (y) minus sine (x) sine (y) EndFraction.
Which list shows the steps in the correct order?
I --> II --> IV --> III
I --> IV --> II --> III
III --> I --> II --> IV
III --> I --> IV --> II
Answers
Answer:
The answer is B: I IV II III
Step-by-step explanation:
Just did it
The sequence for the derivation of tangent sum identity is option I --> IV --> II --> III.
What is trigonometric identity?The trigonometric identities is the relationship between the different trigonometric ratios. These trigonometric identities are the basic formulae that are true for all the values of the reference angle.
For the given situation,
The derivation for the tangent sum identity is given in the table below.
The derivation follows the steps,
[tex]\frac{sin(x+y)}{cos(x+y)}[/tex]
we know that, [tex]sin(x+y) = sinx cosy + cosx siny[/tex] ,
[tex]cos(x+y)=cosxcoxy - sinxsiny[/tex] and
[tex]\frac{sinx}{cosx}=tanx[/tex]
⇒ [tex]\frac{sinxcosy + cosxsiny}{cosxcosy-sinxsiny}[/tex]
Divide each term by [tex]cosxcosy[/tex]
⇒ [tex]\frac{\frac{sinxcosy}{cosxcosy} +\frac{cosxsiny }{cosxcosy} }{\frac{cosxcosy}{cosxcosy} -\frac{sinxsiny}{cosxcosy} }[/tex]
⇒ [tex]\frac{tanx+tany}{1-tanxtany}[/tex]
Hence we can conclude that the derivation of tangent sum identity is option I --> IV --> II --> III.
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Related Questions
HELP ASAP
Given f(x)= -5x +2 and g(x)= x +4, find (f •g)(x)
Answers
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[tex]f(x) = - 5x + 2[/tex]
[tex]g(x) = x + 4[/tex]
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[tex](f \times g)(x) = f(x) \times g(x)[/tex]
[tex](f.g)(x) = ( - 5x + 2)(x + 4)[/tex]
[tex](f.g)(x) = - 5 {x}^{2} - 20x + 2x + 8 \\ [/tex]
[tex](f.g)(x) = - 5 {x}^{2} - 18x + 8 [/tex]
Done...
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Answer:
f (x+4) = -5x -18can someone check my account to help me on my newest math problems?
CORRECT ANSWERS ONLY
wrong ones will be reported instantly
Answers
Answer:
Absolutely, I would be more than willing to.
Which expression is equivalent to 17s - 10 + 3(2s +1)?
Answers
Answer:
7s
Step-by-step explanation:
17s-10=3(2s+1)
17s-10 = 7s
2s+1=3s
7s+3s=10
10-3=7s
IM STUCK i need help WITH THIS PROBLEM THE NUMBER 4 will give brainly
Answers
Answer:
Ok say your social life is on that scale, Now the moment you walk into school your life is A which means it hasn't made it anywhere..now as you progress your love life goes up and becomes a B soon you grow popular and hit C as your results sky rocket..suddenly something you do affects that maybe a bad grade or something you did to someone then your social life drops dramatically to a D and soon crumbling to an E.
~ Zachary Mark brainliest if you want Thanks <3 Have a nice day!!!
Answer:
The depth of water in a stream bed over time
Step-by-step explanation:
Caitlyn was drawing in Art class. She had 20 hearts and 15 flowers.
What is the ratio of flowers to hearts?
Answers
Answer:
15:20
Step-by-step explanation: Well we know that we have 20 hearts and 15 flowers. In the question, it mentions flowers first so we put the flowers first in the ratio. flowers:hearts or 15:20
15 : 20 hope it helped:)
Find −7(9m−2)+(−5+6m).
Answers
- 57m + 9
Step-by-step explanation:Hi there !
−7(9m − 2) + (−5 + 6m) =
= -7×9m - 7×(-2) - 5 + 6m
= - 63m + 14 - 5 + 6m
= - 57m + 9
Good luck !
What’s the answer for this 3x+6x-4
Answers
Answer:
9x-4
Step-by-step explanation:
Add 3x and 6x hope it help
Answer:
9x - 4
Step-by-step explanation:
3x + 6x - 4
First, combine like terms, so you would add 3x and 6x together to form 9x
9x - 4
Because you cannot simplify this equation any more, that is the answer
I hope this helps :)
What is 0.5, 3/16, 0.75, 5/48 to Least to greatest?
Answers
Answer
5/48, 3/16, 0.5, 0.75
Step-by-step explanation:
If Dan earns $35 for 7 hours of work, what is his unit rate of earning? *
Answers
Answer:
$5 an hour
Step-by-step explanation:
refer to image
write an equation that passes through (2,3) with a slope of 5
Answers
Answer:
7
Step-by-step explanation:
y=mx+c put the value of
x=2,y=3 and m=5 and solve this and you will get the answer of c=7
1-2 [-3/2 (8/9) +11]
Answers
Answer:
Your answer is:
Simplify:
Exact Form: -55/3
Decimal: 18.3
Mixed Fraction: -18 1/3
Step-by-step explanation:
Hope this helped : )
How do I do this? I need a quick answer please!
Answers
Answer:
I cant really see
Step-by-step explanation:
I advise you to first see if its a right angle and then maybe see how many inches the point are apart :))) hope I help
Simplify 50/780 if possible
Answers
Answer: 5/78
Step-by-step explanation: u simplify
Answer:
5/78
Step-by-step explanation:
Divide both parts by 10.
Hope I helped :)
2) Ruth borrows $440 at 0.6% simple interest per month. When
Ruth pays the loan back 4 years later, how much interest does
Ruth pay?
Answers
Answer:
$10.56
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 0.6%/100 = 0.006 per year,
then, solving our equation
I = 440 × 0.006 × 4 = 10.56
I = $ 10.56
The simple interest accumulated
on a principal of $ 440.00
at a rate of 0.6% per year
for 4 years is $ 10.56.
Answer:
450.56
Step-by-step
440 x 0.006 x 4 + 440 =450.56
please help........ yup
Answers
Answer:
The amberjack weighed 23 pounds, the kingfish 46 pounds, the marlin 92 pounds and the tarpon 115. pounds.
Roberta is planting flowers in her garden. She plants 9 rows of flowers. There are 7 flowers in each row. How many flowers does she plant in all?
Answers
Answer:
63 flowers
Step-by-step explanation:
all you have to do is multiply 7 and 9
-(4) to the power of 2
Answers
Answer:
-16
To learn more, take a look at the chart below, thanks.
Which shape has a larger area: a rectangle that is 7 inches by 34 inch, or a square with a side length of 212 inches? Show your reasoning.
Answers
Answer:
Area of the rectangle = l×b
= 7×34 = 238sq.inches
Area of the square = side ²
= 212² = 44,944sq.inches
Therefore, the square has a larger area
HELP HELP I NEED HELP ASAP
Graph y-7=-3(x-1).
Answers
the coldest temperature on record in town A is -3.33 degrees Fahrenheit. The coldest temperature on record in town B is -3 2/5 Fahrenheit. Which town has the colder temperature?
Answers
Answer:
town b
Step-by-step explanation:
-3.33 degrees is smaller than 2/5 of 1.00 because 2/5 is 0.4 so -3.4 degrees is colder than -3.33.
Is this true 2.01 < 2.2
Answers
Answer: True
Let's make 2.2 into a three digit number to calculate and focus better.
⇒ 2.01 < 2.20
2.20 is 0.19 more than the number/decimal 2.01.
So, the answer is True. 2.2 is greater than 2.01.
Which point is a solution to the inequality shown in this graph?
O A. (0,-5)
B. (5,-5)
C. (3, -1)
O D. (0,0)
Answers
(3, -1) is a solution to the inequality shown in this graph.
What is solution to an inequality?Any point inside or boundary of feasible region is called a solution of inequality.
The point (3, -1) lies on boundary of feasible region.
Hence, (3, -1) is a solution to an inequality shown in this graph.
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A breakfast cereal comes in two different sized packages. The 8-ounce box costs $2.88 while the 12-ounce box costs $3.60. Which is the better buy? How much does the better buy cost per ounce?
Answers
Answer: the 12 once box
Step-by-step explanation:
8- once box =.36 and the 12 once box is =.3
Answer:
(12-ounce box) $0.30
Step-by-step explanation:
2.88 divided by 8 = $0.36 per ounce
3.60 divided by 12 = $0.30 per ounce
MATH HELP ME ASAP PLEASE
Answers
Answer:
53lbs.
Step-by-step explanation:
If Kevin bought 3 20lbs. Bags of gravel he would have 60 lbs. of gravel. In the end he has 7 lbs. of gravel left he used 53 pounds.
Equations:
7+x=60 or 60-7=53 lbs.
Answer:
3 pounds of gravel
Step-by-step explanation:
If you look at the chart, each bag of gravel is 20 lbs. If he bought 4 then that is 20 x 4. That equals 80. If he only used 77 pounds of it, then you get 80-77. That equals 3
In the diagram below, FAD || EHC, and ABH and BC are drawn. F А B H C If mZFAB = 48° and mZECB = 18°, what is mZABC? 1) 18° 2) 48° 3) 66° 4) 114° O Option 1 O Option 2 O Option 3 O Option 4
Answers
Answer : (3) 66°
Step-by-step explanation:
180 - (48 + 66)
180 + 114
=66
The measure of m ZABC is 66 degrees.
We have given that,
In the diagram below, FAD || EHC, and ABH and BC are drawn. F А B H C If mZFAB = 48° and mZECB = 18°.
We have to determine mZABC
What the angle?
An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
180 - (48 + 66)
180 + 114
=66
Therefore the measure of m ZABC is 66 degrees.
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Write the equation of the line that passes through the points (7,-9) and (2,1). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line
Answers
Answer:
y=-2x+3
Step-by-step explanation:
see the attached above.
I really sorry if you can't read me what I have done.
Best of luck :-)
Can you please help solve this problem Find m
Answers
Answer:
where is your question boy /girl tell me
R(4, 2) and S(10, 10) are the endpoints of a line segment. What is the midpoint M of that line segment?
Write the coordinates as decimals or integers.
M = (, )
Answers
M = (7,6)
Step-by-step explanation:
formula to find mindpoint is
[tex](\frac{x2 + x1}{2} \frac{y2 + y1}{2} )[/tex]
(4,2) = (x1, y1)
(10,10) = (x2,y2)
now substitute those into the formula!
[tex]\frac{10 + 4}{2} \frac{10 + 2}{2} [/tex]
now solve for x & y !!
[tex]x = \frac{10 + 4}{2} = \frac{14}{2} = 7[/tex]
[tex]y = \frac{10 + 2}{2} = \frac{12}{2} = 6[/tex]
so now that we have solved for x & y put it in point form and your done !!
point for is (x,y)
and thanks why the Midpoint is (7,6)
Consider the functions f(x) = 2x + 9 and g(x) = (x - 9)/2. Calculate the following.
A. g( f( 15)) B. g( f( -3)) C. g( f( x))
Answers
9514 1404 393
Answer:
A. 15
B. -3
C. x
Step-by-step explanation:
C. Since we want different values of g(f(x)), it is convenient to find that first.
g(f(x)) = g(2x +9) = ((2x +9) -9)/2 = 2x/2
g(f(x)) = x
__
A. g(f(15)) = 15
__
B. g(f(-3)) = -3
Mrs. Owens bought two candle holders for her dining room table. She paid with a $100 bill and received $32.16 in change. If sales tax is charged at a rate of 6%, what was
the price for one candle holder before taxes?
Drag and drop an answer choice into each empty box below.
$32.00 $32.16 $33.92 $63.76
The price of one candle holder before taxes was
Answers
Answer:
$32.00
Step-by-step explanation:
100-36.12 = 67.84 - That's how much she paid for 2 after tax.
So let's eliminate the wrong answers:
63.76*2 is way over 100 so it's not that
33.92*2 is 67.84, but the question asks before taxes so it's not that
32.16*2 is 64.32, but there is tax so we must multiply it by 1.06. 64.32*1.06 is 68.18
32*2 is 64. 64*1.06 is 67.84. There for the correct answer is $32.00