Answers
Answer: see proof below
Step-by-step explanation:
Given: A + B = C → A = C - B
→ B = C - A
Use the Double Angle Identity: cos 2A = 2 cos² A - 1
→ (cos 2A + 1)/2 = cos² A
Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · 2 cos [(A - B)/2]
Use Even/Odd Identity: cos (-A) = cos (A)
Proof LHS → RHS:
LHS: cos² A + cos² B + cos² C
[tex]\text{Double Angle:}\qquad \dfrac{\cos 2A+1}{2}+\dfrac{\cos 2B+1}{2}+\cos^2 C\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}\bigg(2+\cos 2A+\cos 2B\bigg)+\cos^2 C\\\\\\.\qquad \qquad \qquad =1+\dfrac{1}{2}\bigg(\cos 2A+\cos 2B\bigg)+\cos^2 C[/tex]
[tex]\text{Sum to Product:}\quad 1+\dfrac{1}{2}\bigg[2\cos \bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A-2B}{2}\bigg)\bigg]+\cos^2 C\\\\\\.\qquad \qquad \qquad =1+\cos (A+B)\cdot \cos (A-B)+\cos^2 C[/tex]
[tex]\text{Given:}\qquad \qquad 1+\cos C\cdot \cos (A-B)+\cos^2C[/tex]
[tex]\text{Factor:}\qquad \qquad 1+\cos C[\cos (A-B)+\cos C][/tex]
[tex]\text{Sum to Product:}\quad 1+\cos C\bigg[2\cos \bigg(\dfrac{A-B+C}{2}\bigg)\cdot \cos \bigg(\dfrac{A-B-C}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1+2\cos C\cdot \cos \bigg(\dfrac{A+(C-B)}{2}\bigg)\cdot \cos \bigg(\dfrac{-B-(C-A)}{2}\bigg)[/tex]
[tex]\text{Given:}\qquad \qquad =1+2\cos C\cdot \cos \bigg(\dfrac{A+A}{2}\bigg)\cdot \cos \bigg(\dfrac{-B-B}{2}\bigg)\\\\\\.\qquad \qquad \qquad =1+2\cos C \cdot \cos A\cdot \cos (-B)[/tex]
[tex]\text{Even/Odd:}\qquad \qquad 1+2\cos C \cdot \cos A\cdot \cos B\\\\\\.\qquad \qquad \qquad \quad =1+2\cos A \cdot \cos B\cdot \cos C[/tex]
LHS = RHS: 1 + 2 cos A · cos B · cos C = 1 + 2 cos A · cos B · cos C [tex]\checkmark[/tex]
Related Questions
are u a freak(math wise)
Answers
Answer:
nope
Step-by-step explanation:
because i am dumb
I need help with these questions will give brainiest
Answers
Answer:1F= f(x)=3x+1.5y
1E=18
1A domain=3 range=1.5
Step-by-step explanation:
Another one help please
Answers
there must be subtraction of multiplication of each two diagonal,
|G|=[12×2-(-6)×0]
=(24+0)
=24ans
Answer:
Option B). 24
Explanation:
Refer to the attachment for your solution.
What
is
the
solution
to
the
equation?
5x – 4 = 3x + 10
Answers
Answer:
x = 7
Step-by-step explanation:
5x - 4 = 3x + 10
Combine Like Terms
2x = 14
Divide
x = 7
3^-4=????? HURRRRYYYYYYYYYYYYYYYYY
Answers
Answer:
Here’s the answer :)
Step-by-step explanation:
Answer:
[tex] {81}^{ - 1} \: or \: \frac{1}{81} [/tex]
Step-by-step explanation:
[tex] {3}^{ - 4} [/tex]
Apply rule :
[tex] {a}^{ - 1} = \frac{1}{ {a}^{1} } [/tex]
[tex] \frac{1}{ {3}^{4} } = \frac{1}{81} \: or \: {81}^{ - 1} [/tex]
!!!! I NEED HELP RIGHT NOW ITS DUE IM 5 MINUTES !!!!
Answers
Answer:
Step-by-step explanation:
A = h(a+b)/2 for h
2A = h(a + b)
h(a+b) = 2A
h = 2A/(a+b)
Find variable of b + 25 = b —25
Answers
Answer:
There is no solution
Step-by-step explanation:
Simplifying
b + 25 = b + -25
Reorder the terms:
25 + b = b + -25
Reorder the terms:
25 + b = -25 + b
Add '-1b' to each side of the equation.
25 + b + -1b = -25 + b + -1b
Combine like terms: b + -1b = 0
25 + 0 = -25 + b + -1b
25 = -25 + b + -1b
Combine like terms: b + -1b = 0
25 = -25 + 0
25 = -25
Solving
25 = -25
Couldn't find a variable to solve for.
This equation is invalid, the left and right sides are not equal, therefore there is no solution.
Answer:
There are no values of b no solution that makes the equation true.
Step-by-step explanation:
How do I find the domain and range of a graph?
Answers
The domain is the x-axis and the range is the y-axis.
To find the domain, you measure or count the widest part of this oval horizontally. So that is 3 units to the right of 0 and 3 units to the left of 0. I counted it exactly on the axis because that is the widest part of the oval.
To find the range, you again count or measure the widest part of the oval vertically. So that is 4 units above 0 and 4 units below 0.
Final Answer
D: -3 ≤ x ≤ 3
R: -4 ≤ x ≤4
Cual es el perímetro de un rectángulo, si se sabe que el largo mide 6 cm y su ancho, 4 cm?
Answers
Answer:
20
Step-by-step explanation:the trabslation is 'whats the perimiter of a rectanglr if its lenght is 6cm and its width is 4cm'
HELP ME PLS
A media research survey showed that one evening, 2/3 of all U.S. households had their televisions on, and 3/8 of them were watching a World Series baseball game. What fraction of the U.S. households was watching the game?
Answers
Answer:
sfhjty
Step-by-step explanation:
For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation that will represent the cost.
Answers
what is (4x^2y^3)^2=
Answers
16x⁴y⁶
Step-by-step explanation:(4x²y³)² =
= 4²x²ˣ²y³ˣ²
= 16x⁴y⁶
Anyone??
Which is the best estimate of
-18
-9
9
18
Answers
Answer:
18
Step-by-step explanation:
I'd did poses of elomanation
Answer:
d
Step-by-step explanation:
Please help Factor the expression using the GCF the expression 32z-48 factored using the GCF is
Answers
Answer:
16(2z -3)
Step-by-step explanation:
There are two ways of solving this problem.
List out the factors of the numbers:
32z - 48
= 32 * z - 48
32= 1, 2, 4, 8, 16, 32
48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
the largest common factor that both numbers have in common is 16,
So factoring the equations means the one has to divide the equation by 16 and write it outside of the parenthesis.
16 * ( 2 * z - 3)
16(2z -3)
Another way of solving the problem:
prime factorize the number:
32 = 2^5
48 = 2^4 * 3
Both numbers have 2^4 as their largest factor in common meaning that that is their GCF. 2^4 is 16.
Now factor out 16 and write it on the outside of the parenthesis.
16 * ( 2 * z - 3)
16(2z -3)
Answer:
16(2z -3)
Step-by-step explanation:
In how many ways can 11 bowlers be
selected from 25 who came to a bowling ally?
using npr or ncr
Answers
Answer:
Yes ans = 27720. Total possibilities = C(4,1) * C(6,4) * C(11,6) = 27720.
please help me out ! I am stuck
Answers
Answer:
5x =324
Step-by-step explanation:
[tex]5x \div 9 =36\\\\5x = 36\times 9\\\\5x = 324[/tex]
Help ASAP please and explain why ?!
Answers
Answer:
It is C, because to find volume you must use the formula l×w×h, or length times the width times the height. (cm^3)
Answer:
C
Step-by-step explanation:
Unlike area that's cm² because it's like A= L*W
Volume is cm³ because it's like A= L*W*H
Help me please!!!!!!!!!!!!!!!
Answers
Answer:
The answer is D
Step-by-step explanation:
There are 6 black circles and 2 red circles which could be written as 6 + -2, the positive sign from will turn into a negative bc if the -2, so then it would be 6-2=4
24 - x = 32 , what is it he answer to this please !
Answers
Answer:
- 8
Step-by-step explanation:
Step 1:
24 - x = 32
Step 2:
- x = 32 - 24
Step 3:
- x = 8
Answer:
x = - 8
Hope This Helps :)
-2/5 + 1/2 please help guys I really need it
Answers
Answer:the answer is 1/10
Step-by-step explanation:
Dave is driving to Dallas, TX for the weekend from Austin, TX for the weekend. He is traveling along the tollway 130. The speed limit is 80 mph. There are approximately 1.6 kilometers in 1 mile. What is this limit in kilometers per hour?
Answers
We need to multiply the 80mph by the 1.6 to make it KPH
When done correctly we get the answer of 128KPH
The limit is 128kph
HOPE THIS HELPED. DONT FORGET TO MARK THIS AS THE BRAINLIEST ANSWER AND GIVE IT A 5 STAR SO OTHER PEOPLE CAN BE HELPED BY THIS ANSWER!! HAVE A NICE DAY!
Which choices are correctly written in scientific notation? Check all that apply
17.1 times 10 Superscript 3
8.05 times 10 Superscript 3
6.25 times 4 Superscript 3
4 times 10 Superscript negative 16
22.09 times 10 Superscript negative 9
3.03 times 10 Superscript negative 1
5 times 10 Superscript 10
3.44 times 1 Superscript 10
Answers
Simon is making a poster about friendship in his art class. He divides his poster into 3 equal parts. Simon writes the names of his friends all over each part. Simon uses 1 part for his neighborhood friends and 1 part for his friends from school.
What fraction of the poster does Simon use for his friends from school?
Answers
Answer:
1/3
Step-by-step explanation:
The most important thing to remember is that the poster is divided into three equal parts and 1 part of it is for his neighborhood friends and another one part of it is for his friends from school. The denominator would be three and the numerator would be the 1 part he uses for his friends from school.
What are the solutions 2x^2-16x34=x^2-6x+10 check all of the boxes that apply
Answers
Answer:
x=−3+√563
or/and
x=−3−√563
Step-by-step explanation:
HELPPPPPPPP
An angle formed by the intersection of two lines is obtuse. Could the lines be perpendicular? Explain.
Answers
Answer:
no
Step-by-step explanation:
because when lines are perpendicular, the angles are 90 degree angles.
You want to buy a new hat that costs $9.20 on the price tag. How much
will you pay at the register if there is an 8.5% tax? Round to the nearest
cent. *
Answers
Answer:
$9.98 :)
Step-by-step explanation:
just multiply the tax (0.085) by the price ($9.20) then add the initial price ($9.20) to that.
Solve for 3x + 5(x - 2) = 14
Answers
3x+ 5x - 10 = 14
8x-10= 14
add 10 to both sides
8x=24
divide 8 both sides
x = 3
I am not sure what the answer is to this question. | x - 1 | + 5 = 2 can you please help?
Answers
Answer:
The answer is 4
Step-by-step explanation:
I hope it helps I had to do the math
10 pts
The price of a video game was reduced from $60 to $45. By what percentage was the price of
the video game reduced?
Answers
Answer: It was reduced by 25%
Step-by-step explanation: to go from $60 to $45, you would've gone down $15. 15, or $15, if 1/4 of 60, or $60. 1/4 also is 25%, so the price would have gone down by 25%.
I was reading a book last night that said about 2/3 of Americans attend college, and about 40 percent of those actually graduate. So, about what percent of Americans actually earn college degrees?
Answers
Answer:
26.67% Of Americans earn college degrees.
Step-by-step explanation:
[tex]\frac{2}{3} *40 = 26.67[/tex]