Question: Using only reciprocal, Pythagorean, sum/difference, and/or half angle identities, prove the equation below. You must use angles A and B, do not replace with actual vales. Only work with the right side of the equation. You should use TEN steps to accomplish this proof! cosA+cosB= 2cos(A+B/2)cos(A-B/2)
Answer:
See explanation below
Step-by-step explanation:
Recall the identity for the cosine of an addition of angles:
[tex]cos(\theta+\gamma)= cos(\theta)*cos(\gamma)- sin(\theta)*sin(\gamma)[/tex]
and that for a subtraction of angles:
[tex]cos(\theta-\gamma)= cos(\theta)*cos(\gamma)+sin(\theta)*sin(\gamma)[/tex]
Now, use the property of addition of angles above to write :
[tex]cos(\frac{A+B}{2} +\frac{A-B}{2} )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )-sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )[/tex]
but since : [tex]\frac{A+B}{2} +\frac{A-B}{2}= A[/tex]
Then the cosine of addition of angles above can be written as:
[tex]cos(\frac{A+B}{2} +\frac{A-B}{2} )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )-sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\\cos(A)=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )-sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )[/tex]
We do something similar now with the cosine of the subtraction of angles:
[tex]cos(\frac{A+B}{2} -\frac{A-B}{2} )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )+sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )[/tex]
and we notice that: [tex]\frac{A+B}{2} -\frac{A-B}{2}= B[/tex]
Then the cosine of subtraction of angles above can be written as:
[tex]cos(\frac{A+B}{2} -\frac{A-B}{2} )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )+sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\\cos(B )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )+sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )[/tex]
and finally, we add term by term the expressions we got for cos (A) and for cos(B) and notice that the terms that contain the sine functions cancel each other because they have opposite signs, while the terms in cosine add up to double themselves:
[tex]cos(A )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )+sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\\+\\cos(B )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )-sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\\=\\cos(A) +cos(B)=2\,cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )[/tex]
which is what we wanted to prove.
If you flip 3 coins what is the probability of NOT getting three Heads? P(not getting 3 Heads)
Answer:
Yeah im sure you wont get 3 heads for all coins it would usually be like 1 tails, 2 tails or 3 tails :/?
Step-by-step explanation:
Ina crespo rowed 7.5 miles down the Hanbashabee river in 1.5 hours ,but the return trip took her 2.5 hours.find the rate ina rows in still water and the rate of the current.
Answer:
rate of current=1 mph
Step-by-step explanation:
which rule best described the following pattern 5,6,15,16,25,26,35
What is the slope of a line passing
through points (-6, 3) and (-3, -1)?
Answer:
-4/3
Step-by-step explanation:
you do change in y over change in x which is -1-3 over -3-(-6)
when you do the calculations you get -4/3
cooper's jump rope is for 4 2/5. luke's jump rope is 4 3/4 ft long. whose jump rope is longer? how much longer? show your work
Answer:
Juke's jump; by 0.35 feet
Step-by-step explanation:
Given that,
Cooper's jump rope is for [tex]4\dfrac{2}{5}[/tex] feet.
Juke's jump rope is [tex]4\dfrac{3}{4}[/tex] feet.
Cooper's jump is :
[tex]4\dfrac{2}{5}=\dfrac{22}{5}\ \text{feet}\\\\=4.4\ \text{feet}[/tex]
Juke's jump is
[tex]4\dfrac{3}{4}=\dfrac{19}{4}\\\\=4.75\ \text{feet}[/tex]
So, it is clear that Juke's jump is longer than Cooper's jump.
Juke's jump - Cooper's jump = 4.75 - 4.4
= 0.35 feet
or
So, Juke's jump is 375 feet longer.
which of the following are true of linear functions?
Answer:
1. 3. 6.
Step-by-step explanation:
Answer:
There is exactly one output for each input.
The graph of a linear function is a straight line.
A linear function has a constant rate of change.
Step-by-step explanation:
The Kuiper Belt is estimated to be about 3,000,000
meters wide. Which value represents the estimated width of the Kuiper Belt, in meters, in scientific notation?
Answer:
the answer will be 12 bc all you do is divided 6.6 =11
Step-by-step explanation:
The scientific notation for the given width will be [tex]3*10^{6}[/tex].
What is scientific notation?A method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy.
Given that, The Kuiper Belt is estimated to be about 3,000,000
meters wide.
3,000,000 = 3x1000,000
= [tex]3*10^{6}[/tex].
Hence, The scientific notation for the given width will be [tex]3*10^{6}[/tex].
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87.039 as a mixed number
Answer:
87 39/1000
Step-by-step explanation:
will give brainliest!!!! The value of the 5 in the number 594,631 is how many times larger than the value of the 5 in the number 859,463? *
Answer:
It's 10 times larger.
Step-by-step explanation:
If you just have 500,000, and the other one is 50,000, That means 50,000 x 10 is 500,000.
How do you write three hundred and sixty seven thousand, seven hundred and fifty two?
Answer:
367,752 would be the answer
Answer:
367 750
Step-by-step explanation:
u start and end up with the last number after the another
a boat can travel 384 miles on 48 gallons of gasoline. how much gas does will it need to go 456 miles?
nothing nothing nothing nothing
Answer:
nothing nothing nothing nothing
Step-by-step explanation:
nothing nothing nothing nothing nothing nothing nothing nothing
stream positons by ariana grande <3
Could i get any help here?
Answer:
You will need to figure out how much it is going up by
Step-by-step explanation:
Rewrite the expression in the form a^n
Answer:
a7/5
Step-by-step explanation:
Please help fast!! Is this a function?
Answer:
It's not a function..
Step-by-step explanation:
Just take a look at it.
what did u studied about functions before doing this type of problem in math?
Does it look like it? no.
Answer:
That looks very hard .. sorry :(
Step-by-step explanation:
Solve five ninths plus four sixths. Answer this and ill give brainliest
Answer:
Step-by-step explanation:
(Decimal: 1.222222)
for the below question assume no duplicated units are allowed all the answers for a 5 question multiple choice test are a b c d find the number of possible answer keys a teacher could have
Answer:
4
Step-by-step explanation:
1 2 3 4 so 4 because 4 is the last number before 5
Captain America's circular shield has a diameter of 76.2 centimetres. What is the area of his shield?
Answer:
Its area is 370 square centimeters.
Step-by-step explanation:
brainliest will be given if correct
Answer:
10
Step-by-step explanation:
im not sure if its correct but area is the area around the trapezoid and i added them
1. When developing an interval estimate for the difference between two sample means, with sample sizes of n1 and n2, A. n1 must be equal to n2 B. n1 must be smaller than n2 C. n1 must be larger than n2 D. n1 and n2 can be of different sizes
Answer:
D. n1 and n2 can be of different sizes
Step-by-step explanation:
When we are trying to develop interval estimate for difference between two populations, we first select two samples from these populations. We get the interval using the required statistic.
These are:
- Sample size of both populations. Which are n1 and n2 respectively.
- then the Sample mean of two populations
- sample standard deviation.
The samples of different sample sizes can be used and we are not obligated to make use of the same sample size.
if the number of different schedules is represented by three consecutive even integers, what is the expression for that total number of schedules they have to choose from?
Answer:
s
Step-by-step explanation:
s
sergio must ride 7.5 miles in 1/4 hour to achieve this target speed, so he needs to ride an additional ____ mile per 1/4 hour
Answer: 7.0
Step-by-step explanation:
sergio must ride 7.5 miles in 1/4 hour to achieve this target speed so he needs to ride an addititonal 9.8 mile per1/4 hour
Answer:
30 mph
Step-by-step explanation:
since it is 1/4 you would multply 7.5 times 4, which adds up to 30.
A recipe for 12 bran muffins calls for one cup of flour the number of muffins that can be made varies directly with the amount of flour used there are two 2/3 cups of flour available how many muffins can be made
Answer: 8
Step-by-step explanation:
12 bran muffins in 1 Cup so for 2/3 it is
2/3*12 = 8
Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3?
Answer:
Option 2: [tex]y - 2 = \frac{1}{3}(x-3)[/tex] is the correct answer.
Step-by-step explanation:
The equation of a line with given point(x1,y1) and slope m is given by:
[tex]y-y_1 = m(x-x_1)[/tex]
The line passes through (x1,y1)
Given
[tex](x_1,y_1) = (3,2)\\m = \frac{1}{3}[/tex]
=> x1 = 3
=> y1 = 2
Putting the values of x1, y1 and slope(m) in the point-slope form, the equation of line is:
[tex]y - 2 = \frac{1}{3}(x-3)[/tex]
Hence,
Option 2: [tex]y - 2 = \frac{1}{3}(x-3)[/tex] is the correct answer.
HELP!!!!! PLEASE! The length of 1 year on Uranus is a little more than 84 years on Earth. About how many Uranus years are equal to 175 Earth years?
Answer:
About 2.08 Uranus years is equal to 175 Earth years
Step-by-step explanation:
1 = ?
84 175
175/84 = 2.08
Number of Uranus years are equal to 175 Earth years is 2.08 years.
Given that, The length of 1 year on Uranus is a little more than 84 years on Earth.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Let the number of years be x
1 : 84 :: x : 175
⇒ 1/84 = x/175
⇒ 84x=175
⇒ x=175/84
⇒ x=2.08 years
Therefore, number of Uranus years are equal to 175 Earth years is 2.08 years.
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Venn diagram is shown below:
What are the elements of (A ∩ B) ' ?
Answer:
1 and 2 are the elements of (A B)
Help please!!! I need answers!!!
Answer:
a)
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
I know for sure.
12+84=96
12*1=12
12*7=84
based on the regression output which of the following is the predicted time in minutes that it took to gather the items if the order had 22 items
Answer:
63.89
Step-by-step explanation:
my teacher went over this in class
there is only three options someone help
Answer:
Answer is Option 2
Step-by-step explanation:
Triangles equal to 180 degrees in total. So it is 55+54+x+74=180
The simplified version that I just wrote is Option 2