if cos theta + sin theta = root 2 cos thetha prove that cos theta - sin theta = root 2 sin theta
Answers
Answer:
We have:
If:
Cos(θ) + Sin(θ) = √2*cos(θ)
We want to prove that:
Cos(θ) - Sin(θ) = √2*Sin(θ)
Well, let's start with the first relation:
Cos(θ) + Sin(θ) = √2*cos(θ)
Now we can subtract 2*Sin(θ) and we will get:
Cos(θ) + Sin(θ) - 2*Sin(θ) = √2*cos(θ) - 2*sin(θ)
Cos(θ) - Sin(θ) = √2*cos(θ) - 2*sin(θ)
Now, we also can rewrite the first equation as:
Cos(θ) + Sin(θ) = √2*cos(θ)
Cos(θ) - √2*cos(θ) = - Sin(θ)
Cos(θ)*( 1 - √2) = -Sin(θ)
Cos(θ) = -Sin(θ)/( 1 - √2) = Sin(θ)/(- 1 + √2)
We can replace this in the right side of theequation:
Cos(θ) - Sin(θ) = √2*cos(θ) - 2*sin(θ)
Cos(θ) - Sin(θ) = √2* Sin(θ)/(- 1 + √2) - 2*sin(θ)
Cos(θ) - Sin(θ) = (√2/(- 1 + √2) - 2)*Sin(θ)
Now we have this:
√2/(- 1 + √2)) - 2 = a
if we multiply all by (-1 + √2) we get:
√2 - 2*(-1 + √2) = a*(-1 + √2)
√2 + 2 - 2*√2 = a*(-1 + √2)
2 - √2 = a*(-1 + √2)
√2*(√2 - 1) = a*(-1 + √2)
√2*(√2 - 1)/(-1 + √2) = a
√2 = a
Then:
√2/(- 1 + √2)) - 2 = √2
If we replace this in the equation:
Cos(θ) - Sin(θ) = (√2/(- 1 + √2) - 2)*Sin(θ)
We get:
Cos(θ) - Sin(θ) = √2*Sin(θ)
Which is the thing we wanted to get.
Please find attached herewith the solution of your question.
If you have any query, feel free to ask.
Related Questions
What's 3/5 of 1/4?!!!!! Plz help me!
Answers
Answer:
2.4 or [tex]\frac{12}{5}[/tex]
Step-by-step explanation:
In the divisor (the second fraction) we flip the numerator and the denominator. This is known as the reciprocal and basically it means the reverse of the fraction. When we find the reciprocal, we also have to change the division sign to a multiplication sign.
Once you've flipped the second fraction and changed the symbol from divide to multiply, we can multiply the numerators together and the denominators together and we have our solution:
[tex]\frac{12}{5}[/tex]
En tu cuaderno realiza la conversión de los siguientes decimales a fracciones.
a) 0.250 :
Answers
Answer:
Tengo que convertir los siguientes números decimales a fracciones, y también tengo que simplificarlos a su mínima expresión. Aquí un ejemplo ;)
(no pido que me digan las respuestas, si no que me ayuden a entenderla)
0.44 = 44/100 = 22/50 = 11/25
0.62=
0.29=
2.05=
1.28=
0.08=
0.50=
0.375=
0.60=
0.7=
Step-by-step explanation:
PLEASE HELP!!!!
Question 1 :
The graph of f(x) = x^2 was transformed to create a graph g(x) =f(x)+2.
Which statement about the graphs is true?
The vertex of the graph of g is 3 units to the right of the vertex of the graph of f.
The vertex of the graph of g is 2 units to the left of the vertex of the graph of f.
The vertex of the graph of g is 2 units above the vertex of the graph of f.
The vertex of the graph of g is 2 units below the vertex of the graph of f.
Question 2 :
The graph of f(x)=x^2 was transformed to create the graph of g(x)=(x−3)^2.
Which statement describes this transformation?
a vertical shift up 9 units
a vertical shift down 9 units
a horizontal shift to the right 3 units
a horizontal shift to the left 3 units
Question 3 :
The graph f(x)=x^2 was transformed to create the graph g(x)=−1/5x^2
Which statement describes this transformation?
a reflection over the x-axis and a vertical compression
a reflection over the x-axis and a horizontal compression
a reflection over the y-axis and a horizontal compression
a reflection over the y-axis and a vertical compression
Question 4 :
Use the parabola tool to graph g(x).
g(x)=(x+1)^2−2
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
PLEASE HELP.
Answers
Answer:
the first question is the second choice
the second question is the 1st choice
the third question is the third choice
Solve for x.
4(5x−20)=−20
Enter your answer in the box.
x =?
Answers
Answer:
4(5x-20)=-20 should be x=3
Answer:
x = 3
Step-by-step explanation:
4(5x−20)=−20 | Given
20x - 80 = -20 | Distribute the number on the outside (multiply all numbers on the inside by the number on the outside, 4×5x and 4×-20)
20x = 60 | Add 80 to both sides (do the opposite operation, if its a negative number add it to both sides)
x = 3 | Divide both sides by 20x (20x turns into x and 60 turns into 3 via 60÷20)
If y varies directly as x and x=6 when y=0.5, find y when x=10
Answers
Answer:
y = [tex]\frac{5}{6}[/tex]
Step-by-step explanation:
Given y varies directly as x, then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition x = 6 when y = 0.5 , then
0.5 = 6k ( divide both sides by 6 )
[tex]\frac{0.5}{6}[/tex] = k , that is k = [tex]\frac{1}{12}[/tex]
y = [tex]\frac{1}{12}[/tex] x ← equation of variation
When x = 10, then
y = [tex]\frac{1}{12}[/tex] × 10 = [tex]\frac{10}{12}[/tex] = [tex]\frac{5}{6}[/tex]
Write an algebraic expression for the verbal expression
a number n less 35
Answers
Answer:
Step-by-step explanation:
the expression will be
n-35
Please answer fast ill give brainlist and 5 stars
Halena has a recipe for pastry.
She says that the ratio of margarine to flour is 4:1.
Is Halena correct? Explain your answer.
Answers
Answer:
yes because she adds 4:1.
Step-by-step explanation:
If the function f has five distinct zeros, which of the following could represent the complete graph off in the xy-plane?
Answers
Answer:
The zeros of a function are the points where the graph of the function crosses the x-axis.
Clearly Graph in option D could be the function which has 5 zeroes as it passes through the axis at 5 points.
Step-by-step explanation:
The graph of the function will intersect the x-axis five times. Then the correct option is D.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
If the function f has five distinct zeros.
Then the graph represents the complete graph of the function in the xy-plane will be
We know that the zeroes of the function are the intersection points of the x-axis and the function.
That means the graph will intersect the x-axis five times.
Then the correct option is D.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ2
Hey Lets Get Some In the
Answers
Step-by-step explanation:
in the?¿????????!?????
Answer:
wott?
Step-by-step explanation:
Questions on attached photo.
Answers
Answer:
0
Step-by-step explanation:
Answer:
[tex]y = {11}^{x} [/tex]
3(y + 4) = 3y + 12
is it true or false?
Answers
Answer:
true
Step-by-step explanation: Any value of y makes the equation true. All real numbers Interval Notation: ( − ∞ , ∞ )
A climber starts descending from 506 feet above sea level and keeps going until she reaches 70 feet below sea level. How many feet did she descend?
Answers
Answer:
she descended 436 feet
Step-by-step explanation:pls mark brainliest i really want to move up a ranking
A chameleon is looking for prey. Let positive numbers represent the elevation of prey above the chameleon and
negative numbers represent the elevation of prey below the chameleon
The chameleon spots a fly at 4 m and a grasshopper at - 6 m.
What does an elevation of Om represent in this situation?
Choose 1 answer.
The elevation of the fly
The elevation of the chameleon
The elevation of the grasshopper
Report a problem
Stuck? Watch a video or use a hint.
Answers
Simplify the given equation.
17x - 6 + 3x - 5 = x + 11 + 4x
Answers
Answer:
x = 22/15
Step-by-step explanation:
17x - 6 + 3x - 5 = x + 11 + 4x
= (17x + 3x) (-6 - 5) = x + 11 + 4x
= 20x - 11 = x + 11 + 4x
= 20x - 11 = (x + 4x) + 11
= 20x - 11 = 5x + 11
= 20x - 5x = 11 + 11
= 15x = 22
Exact form: 22/15
decimal: 1.4666666...
mixed number: 1 7/15
+) Colin is playing a video game. He wins 25 points for each gold coin he finds. His goal is to win
more than 200 points. He wants to know how many gold coins he needs to find.
Solve the Inequality 25g > 200
Answers
Answer:
you need to find 8 gold bars
Step-by-step explanation:
PLEASE SOLVE THIS PROBLEM AND I WILL GIVE YOU 20 POINTS AND MAKE YOU BRAINIEST!!!!
Answers
Answer:
its 24
Step-by-step explanation:
24
uhh solve the question? i hope i find some haikyuu stans out there✌️
Answers
Answer and Step-by-step explanation:
[tex](\frac{1.25 - x}{1.25x} ) * 100\\\\\\(\frac{1.25}{1.25x} - \frac{x}{1.25x} ) * 100\\\\(\frac{1}{x} - \frac{1}{1.25} ) * 100\\\\\frac{100}{x} - 80\\\\\\[/tex]
Decreased by 20%
Answer:
YESSSSSS I LOVE HAIKYUU (my favorite ppl in haikyuu are iwaizumi, akaashi, kuroo, oikawa, and kenma- also suna)
Step-by-step explanation:
also 20% is ur answer
Write the ratio 2 3/5 in simplest form.
Answers
Answer:
Already in simplilest form
Which math expression means "an unknown number divided by 180"?
A. X. 180
B. X = 180
C. X- 180
D. x + 180
Helppp
Answers
Answer:
The answer should be, x ÷ 180 or [tex]\frac{x}{180}[/tex]
good luck, i hope this helps :)
HELP ME ASAP!!!!!!!!!!!!!!!
See question attached.
THE CORRECT ANSWER GETS THANKS, A STAR RATING OF EXCELLENT AND BRAINLIEST!!!!!!!!!!!!!!!!! GOOD LUCK!!!!!!!!!!
Answers
Answer:
-1
Step-by-step explanation:
First input = 4
Then we subtract 7 = 4 - 7 = -3
After that we divide 3 = - 3 ÷ 3 = -1
Hence, the output is -1 (Ans)
i giv points please be right
Answers
Answer:
The answer is 84x-16y-10.6
Step-by-step explanation:
You're welcome
What are some things we can comment about this image? Be as specific as possible!
Answers
pls help 72 points given!
Answers
Step-by-step explanation:
x = 1cm. ---- ( tangent property )AB = 2xAB = 2 × 1cmAB = 2cm___________________FOLLOW MEAnswer:
2cm
Step-by-step explanation:
Since x=1 cm, and AB=2x, 2*1=2 cm
A shirt that cost 60 dollars is now on sale for 30% off what is the value of the discount? Using the answer you found to find the difference between the original price and the amount of the discount
Answers
Answer:
you $42 and your saving $18
Step-by-step explanation:
Answer:
$42 would be the cost of the shirt after the discount. The difference between the price of the shirt before the discount, and after is $18.
Step-by-step explanation:
If you divide 60 by 100, you would get the value for 1% of $60. If you multiply that number by the discount amount, you get the amount that is going to be subtracted from the cost when the discount is applied.
60 / 100 = 0.6
0.6 x 30 = 18 (This is the difference)
60 - 18 = 42 (This is the value after the discount)
Thus the value after the discount is $42, and he difference between the 2 values is $18.
Please help! I need it to move on to the next question I have 30 minutes
Answers
Answer:
uh either b or e
the others are slope-intercept
I hope this helps:)
- ♥
Find f(f(x))? Thanks so much!
Answers
f(-3x^2+3x)=-27x^4
Hope this helps
Have a great day or night
ANYONE PLZ ANSWER THE ANGLE!!!!!
Answers
Answer:
b
Step-by-step explanation:
the answer is b. because it just is lolz.
Answer:
A. 45°Step-by-step explanation:
It shows 45°, in the middle point between 40° and 50°
Correct choice is A
Maureen is in charge of renting a climbing wall for the school’s fundraiser. The equation y = 170x represents the total cost of renting a climbing wall from Company A. The table shows the relationship between cost and rental time for Company B. The graph shows the relationship for Company C. Which company, if any, offers the best deal? Explain.
GRAPH COMPANY B:
2 340
3 510
4 680
5 850
GRAPH COMPANY C:
2 350
3 525
4 700
5 875
PLEASE EXPLAIN NOT ONLY SAYING WHICH COMPANY ONLY??!!
Answers
Answer:
Company A and B
Step-by-step explanation:
For company A- 170 is the cost for one hour
For company B- 170 is the cost for one hour
For company C- 175 is the cost for one hour
So company A and B offer the best deal since they both offer $170 per hour.
Write an equation describing the relationship of the given variables. y varies inversely as the cube root of x and when x=125, y=8.
Answers
Answer:
y = 40 / x^1/3
Step-by-step explanation:
Given that :
y α x^1/3
y = k * 1 / x^1/3
y = k / x^1/3
When x = 125 ; y = 8
8 = k / 125^1/3
Cube root of 125 = 5
8 = k / 5
8 * 5 = k ; k = 40
Hence, expression becomes :
y = 40 / x^1/3
y α k/∛x is the relationship of the variables x and y whose values are 125 and 8.
What is Equation?Two or more expressions connected with an equal sign is called Equation.
The relationship of the given variables. y varies inversely as the cube root of x.
By given data we can write as
y α k/∛x
The cube root of 125 is 5.
y α k/∛125
y α k/5
8=k/5
k=40
Hence y α 40/∛x is the relationship of the variables x and y whose values are 125 and 8.
To learn more on Equation click:
https://brainly.com/question/10413253
#SPJ2
Can you guys please help me get the right answer I already got one wrong I can’t get another wrong!❤️
Answers
Answer:
C. The area is 900 square feet
Step-by-step explanation:
A square has four equal sides, and if one side is 30 feet then all sides are 30 feet. The formula for a square is A=s2
A=30 squared
A=900 square feet
Answer:
C) 900 square feet
Step-by-step explanation:
A = s^2
A = 30^2 ->30^2 is the same as 30 × 30
A = 900 square feet