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.
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Related Questions
A
The length of Kathy's rectangular
garden is 4 feet more than the width. If
the perimeter of her garden is 40 feet,
what is the length of Kathy's garden?
Answers
Half the perimeter is the length + the width.
Let the width = x
The length is x + 4. ( 4 feet more than the width)
Now you have x + x + 4 = 20
Combine like terms:
2x + 4 = 20
Subtract 4 from both sides:
2x = 16
Divide both sides by 2:
X = 8
The width is 8 feet
The length is 8 + 4 = 12 feet
Answer:12
Step-by-step explanation:
because im smart
helppppp!!!!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
1.1(1.8)(2.5)=4.95
hello, can i please have help on this question.thank you
Answers
Answer:
y = 4x - 3
Step-by-step explanation:
The equation for a line is y = mx +c
We need to find m which is the gradient:
To do this pick any two coordinates on the line:
(1, 1) and (2, 5)
Next divide the difference of the y coordinates by the difference of the x coordinates:
5 - 1 / 2 - 1
= 4/1 = 4
so our gradient is 4
We'd write that as y = 4x + c
Next we need to find c which is the y-intercept
To do this just simply look for where the line crosses the y-axis
This is -3
So we'd write that as y = 4x - 3
Hope this helps :)
Answer:
y=4x-3
Step-by-step explanation:
it wewnt up 4
the baby value/y interseption was -3
HELP I NEED HELP ASAP
Answers
Answer:
I think its D
Step-by-step explanation:
You can rule out A and B because he would be able to throw it farther than 30 ft do that leaves C and D but davis Couldn't throw a 9.1 lb ball 30 ft so the answer is D
Jennifer needs to use a ladder to clean a second floor window on a building. If the window is 13ft above the ground and the base of the ladder is 4ft from the building, which equation below can be used to determine the length of the
Ladder needed to reach the window
A 42 + 139 = 2
В
4² + x² = 13²
С
132_4? = ?
D
132P = 42
Answers
Answer:
Step-by-step explanation:
we have a right triangle,
to find out the hypotenuse, h
H^2=13^2+4^2
H^2=169+8=177
The required equation would be x² = 13² + 4² which is determined by Pythagoras theorem that is used to the length of the Ladder needed to reach the window.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
What is Pythagoras theorem?Pythagoras theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.
We have given that the window is 13ft above the ground and the base of the ladder is 4ft from the building
As per the condition, We have a right triangle.
To find out the hypotenuse x
By Pythagoras theorem,
⇒ x² = 13² + 4²
⇒ x² = 169 + 8
Therefore, the equation would be x² = 13² + 4²which is used to determine the length of the Ladder needed to reach the window.
Hence, the correct answer would be an option (A).
Learn more about Pythagoras's theorem here:
brainly.com/question/343682
#SPJ2
If a solution to a linear system of equations is no solution, then what must be true about the graph of the system?
Answers
Answer:
Step-by-step explanation:
The lines are parallel to one another.
A linear system of equations has no solution if the graphs are parallel and the two lines never meet.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
There can be one solution to a system of two linear equations, an infinite number of solutions, or no solutions at all. The number of solutions to a system of equations can be used to categorize it.
A system is deemed consistent if there is at least one solution to the problem. A consistent system is said to be independent if it only has one possible outcome.
Thus, a linear system of equations has no solution if the graphs are parallel and the two lines never meet.
Learn more about the equation here,
https://brainly.com/question/10413253
#SPJ6
Given that = 3.14, calculate the circumference of the circle with radius 10cm.
Answers
Using the circumference formula, we get that C=2(3.14)10=62.83
Lena knit a total of 20 centimeters of scarfs over night. How many nights will Lena have to spend knitting in order to knit a total of 50 cm of scarfs. Assume the relationship is directly proportional.
Answers
Answer:
50cm of scarfs is equal to 2.5 nights of knitting.
Step-by-step explanation:
20cm= 1 night
10cm= 1/2 or 0.5 a night
40cm= 2 nights
50cm=2.5 nights
y+1=2(x-4) graph the equation
Answers
M a t h w a y will help you my friend!
I was struggling with math and using it got me get back on track :)
Find the missing angle
Answers
M 2: 49
M 3: 87
M 4: 44
help quickly, please! I'll mark you brainliest if you're right!
Answers
Answer:
C 803.8 in2
Step-by-step explanation:
Answer:
the answer is C 803.8 in2
Step-by-step explanation:
2 (y-1) ≥8
please answer
Answers
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
y ≥ 5
Step-by-step explanation:
Distribute
2y - 2 = 8
+2. +2
2y/2 = 10/2
y = 5
Write a system of linear inequalities represented by the graph.
Inequality 1:
Inequality 2:
Answers
Answer:
x ≥ -1
y < 3
Step-by-step explanation:
Answer:
Inequality 1: x ≽-1
Inequality 2: x ≼ 3
T-T help me I can't think
Answers
Answer:
81 square inches
Step-by-step explanation:
area of a square= s^2
solve this f(x)=1/2|x-1|-1
Answers
Answer:
x1 = -1,x2 =3
Step-by-step explanation:
Find the inverse. Then, graph both the function and its inverse.
y = 3x2
Answers
Answer:
y = 6
may help you i think so
Question 3
The distance from Mason's house to Kevin's house is about 5 x 10 to the power of 5 inches. The distance from Mason's house to Chloe's house is about 8 x 10 to the power of 7 inches
The distance from Mason's house to Chloe's house is how many times greater than the distance from Mason's to Kevin's house?
Answers
9514 1404 393
Answer:
160
Step-by-step explanation:
Your calculator can compute the ratio of distances for you.
[tex]\dfrac{8\times10^7}{5\times10^5}=\dfrac{8}{5}\times10^{7-5}=1.6\times10^2=\boxed{160}[/tex]
Chloe's house is 160 times as far as Mason's house.
Rushi ran 7.35 miles on Monday and 2.29 miles on Tuesday. How many more miles did Rushi run on
Monday than Tuesday?
Answers
Answer:
5.06
Step-by-step explanation:
hope this helps!
[tex] \frac{1}{32} \times \frac{1}{2 {}^{4} } = ( \frac{1}{4} ) {2}^{x} find \: x[/tex]
tell this question
Answers
Answer: x=1/384
Step-by-step explanation: Hope this help :D
PLS PLS PLS HELP 100 POINTS no scamming
Answers
Answer:
parallelogram:
Hexagon:
Triangle:
Step-by-step explanation:
Answer:
uh what is scamming?????
can somebody help me with this please
Answers
Answer:
q=-14
Step-by-step explanation:
6.4x+2.3=47.1 solve for x.
Answers
Answer:
x=7
Step-by-step explanation:
Answer:
X=7
Step-by-step explanation:
1.) Subtract 2.3 from both sides makeing it 6.4x= 44.8
2.) DIvide 6.4 on both sides making it X=7
Fill in the table using this function rule.
y = -3x+5
x:
-4
-2
0
2
Answers
Answer:
x=5/3 or 2
Step-by-step explanation:
A chef has several recipes that use different
amounts of milk. The table shows the number
of batches he had planned to make. He has time
to make only two recipes but wants to use as
much milk as possible. Which two recipes should
he make? Explain. Find the total amount of milk
he will use.
Answers
Answer:
6
Step-by-step explanation:
please solve! thanks!
Answers
Answer:
uhm no
Step-by-step explanation:
Answer:
arc 1 = 108 degrees
angle 2 = 54 degrees
Step-by-step explanation:
180 - 72 = 108 (half circle -72)
draw a line from center of circle to tangent point.
this line is perpendicular to the tangent line.
all radii are equal.
then, triangle made with the new line is isosceles with two equal angles.
those angles are 36 degrees each (180 - 108 = 72, 72/2 = 36)
line drawn from center to tangent point is 90 degrees so:
90 - 36 = 54 degrees
Select the ratio that is not equivalent to 6:16 PLZ AWNSER NOW
1. 3:8
2. 2 to 8
3. 24/48
Answers
Answer:
2. 2 to 8and3. 24/48Step-by-step explanation:
6:16 simplifies to 3:8, not to 2:8. And 24/48 simplifies to 1/2, not to 6:16.
I would appreciate it if you would please mark me brainliest! Have a blessed day!
determine whether each statement is true or false. QR > ST
m m
m
Answers
Answer:
FALSE
Step-by-step explanation:
QR is NOT greater than ST
The image shows that QR = 9 and ST = 10.
Ten's obvi the bigger number so insted of QR > ST it should be QR < ST.
hope this helps :)
- 7r - 3r - 8 = 24.
Answers
Answer:
24
Step-by-step explanation:
1233+12×19÷3=
çözüm bakalım ???
Answers
Answer:
1309
Step-by-step explanation:
1233 + 12 x 19 / 3 =
1233 + 228 / 3 =
1233 + 76 = 1309
Hope that helps!
Answer:
1,309 eso es con la calculadora sale
Determine how many feet each member of Lola's family walked.
Lola's pet turtle walked 10 feet, and then half that length again.
Lola's baby brother walked 3 feet, and then half that length again.
Lola's hamster walked 6.5 feet, and then half that length again.
Lola's mom walked x feet, and then half that length again.
Answers
Step-by-step explanation:
Lola's pet turtle walked 10 feet, and then half that length again. This means that Lola's pet turtle walked:
= 10 + (1/2 × 10) = 10 + 5 = 15 feet
Lola's baby brother walked 3 feet, and then half that length again. Total length walked will be:
= 3 + (1/2 × 3) = 3 + 1.5 = 4.5 feet
Lola's hamster walked 6.5 feet, and then half that length again. Total length walked will be:
= 6.5 + (1/2 × 6.5) = 6.5 + 3.25 = 9.75
Lola's mom walked x feet, and then half that length again. Total length walked will be:
= x + (1/2 × x) = x + 0.5x = 1.5x
Total feet walked by the whole member of the family will be:
= 15 + 4.5 + 9.75 + 1.5x
= 29.25 + 1.5x
Answer:
turtle: 10 + 5 = 15
brother: 3 + 1 1/2 = 4 1/2
hamster: 6 1/2 + 3 1/4 = 9 3/4
Mom: x + 1/2x = 1 [tex]\frac{1}{2}[/tex]x
Step-by-step explanation: