Answers
Answer: see proof below
Step-by-step explanation:
Given: A + B + C = π → A + B = π - C
→ A + C = π - B
Use the Cofunction Identities: sin (π - A) = sin A
sin (A - π/2) = cos A
cos (π/2 - A) = - sin A
Use the Power Reducing Identity: sin ² A - sin² B = sin (A + B) · sin (A - B)
Use the Sum to Product Identity:
sin A - sin B = 2 [cos (A + B)/2] · [sin (A - B)/2]
Proof LHS → RHS:
LHS: sin² A - sin² B - sin² C
= (sin² A - sin² B) - sin² C
Power Reducing: sin (A + B) · sin (A - B) - sin² C
Given: sin (π - C) · sin (A - B) - sin² C
Cofunction: sin C · sin (A - B) - sin² C
Factor: sin C [sin (A - B) - sin C]
[tex]\text{Sum to Product:}\qquad \sin C\bigg[2\cos \bigg(\dfrac{(A-B)+C}{2}\bigg)\cdot \sin \bigg(\dfrac{(A-B)-C}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad \qquad =2\sin C\bigg[\cos \bigg(\dfrac{(A+C)-B}{2}\bigg)\cdot \sin \bigg(\dfrac{A-(B+C)}{2}\bigg)\bigg][/tex]
[tex]\text{Given:}\qquad \qquad 2\sin C\bigg[\cos \bigg(\dfrac{(\pi - B)-B}{2}\bigg)\cdot \sin \bigg(\dfrac{A-(\pi - A)}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =2\sin C\bigg[\cos \bigg(\dfrac{\pi -2B}{2}\bigg)\cdot \sin \bigg(\dfrac{2A-\pi}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =2\sin C\bigg[\cos \bigg(\dfrac{\pi}{2} -B}\bigg)\cdot \sin \bigg(A-\dfrac{\pi}{2}\bigg)\bigg][/tex]
Cofunction: 2 sin C (-sin B) · (cos A)
= -2 sin C · sin B · cos A
= -2 cos A · sin B · sin C
LHS = RHS: -2 cos A · sin B · sin C = -2 cos A · sin B · sin C [tex]\checkmark[/tex]
Related Questions
Please Help!! 10 Points!! Brainliest answer
Answers
Answer:
XW since it matches the same as IH
Step-by-step explanation:
example if it asked another question saying what corresponds with XY. XY is on the last part of the statement so it would correspond with IJ
16+24/8-6 is equal to________
Answers
Answer: The answer is 28. Hope this helps:)
Answer:
-1
hope this helps
plz mark brainleist
Algebra 1 9th grade
-2x=-18/3
Answers
-x = -9/3 ⇨ -3
Since both numbers are negative, the product becomes a positive.
x=3
Hope this helped!
a flag pole that is 10 m talk casts a shadow that is 6 m long. what is the distance from the top of the pole to the end of the shadow
Answers
Answer:
11.66 meters
Step-by-step explanation:
First draw a diagram. See attachment.
We notice that if we draw everything out, we get a right triangle.
The flag pole and its shadow are the two legs, with lengths 10 and 6 meters. We want to find the distance from the top of the pole to the end of the shadow, so we need to use the Pythagorean Theorem, which states that for a right triangle with legs a and b and hypotenuse c:
a² + b² = c²
Here, a = 10 and b = 6, and we want to find c:
a² + b² = c²
10² + 6² = c²
100 + 36 = c²
136 = c²
c = √136 = 2√34 ≈ 11.66 meters
~ an aesthetics lover
Answer:
11.7
Step-by-step explanation:
27x^0y^-2 for x=4 and y=3
Answers
Answer:
A3=44 56-7
Step-by-step explanation:
You are working hard at the local grocery store each weekend. You have decided to put your money in a compound interest bearing account earning 4% per year. How many years would you estimate that it would take for you to double your money
Answers
Answer:
The answer would be 18 years
Step-by-step explanation:
hope this helps:)
if
f(x)=5x+7
and
g(x)=-2x-4
find
f(g(x))=___x+___
Answers
Step-by-step explanation:
F(g(x)) = -10x-13
First blank: -10
Second blank: -13
Find the value of x of this triangle.
Answers
Answer:
12x
Step-by-step explanation:
Answer: x = 35°
Step-by-step explanation:
A triangle adds up to 180°. Therefore, the equation to find the value of x is 110+2x = 180.Subtract 110 on both sides. 2x = 70Divide by 2 on both sides. x = 35°URGENT PLS HELP
BD bisects ABC. Find each of the following
1. Find the measure of angle ABD if the measure of angle ABD = 6x + 4 and
the measure of angle DBC = 8x - 4
2. Find the measure of angle ABC if the measure of angle ABD = 5y - 3 and the
measure of angle DBC = 3y + 15.
Answers
Align the horizontal edge of the protractor with the base of the triangle. Place the center point of the protractor on the vertex of the angle. Follow the side of the triangle until it reaches the angle measurement mark. Note the measurement.
#2 - Simplify the expression. Type your answer with all lowercase letters and no spaces. * 3h - e + 2h - 5e
Answers
Answer:
5h-6e
Step-by-step explanation:
3h - e + 2h - 5e =
= 3h + 2h - e - 5e
= 5h-6e
Answer:
5h - 4e
Step-by-step explanation:
Add 3h and 2h to get 5h then subtract e from 5e which equals 4e
Hope this helps!
William just accepted a job at a new company where he will make an annual salary of
$60000. William was told that for each year he stays with the company, he will be
given a salary raise of $5000. How much would William make as a salary after 5
years working for the company? What would be his salary after t years?
Salary after 5 years:
Salary after t years:
Answers
Answer:
Salary after 5 years: 60000+(5000)5= 85000
Salary after T years: 6000+(5000)t
Step-by-step explanation:
The way that you would find the amount of money needed after 5 years is by multiplying the 5000, since that is William's raise per year, and then adding 60000, which is the original salary.
In order to find William's salary after t years, since you do not have a number, but have t, you would want to multiply 5000, which is the yearly raise, and t, hich can be any amount of years. After that, you would want to add William's original income to find an answer.
alessialol I will add you back on snap and um I forgot y password to my other acc. so ya and whats the google classroom code?
sorry people but if you will just leave me alone bc im mad at some people
Answers
um ok.........................
Write an expression to represent the perimeter of the triangle below in simplest form
Answers
Answer:
Perimeter of the given triangle = [tex]\frac{7x+38}{(x+8)(x+5)}[/tex] units
Step-by-step explanation:
Perimeter of a polygon = Sum of the measures of all sides of the polygon
From the picture attached,
Perimeter of the given isosceles triangle = Measures of two equal sides + remaining side
P = [tex]2(\frac{3}{x+8})+\frac{x}{x+5}[/tex]
= [tex]\frac{6}{(x+8)}+\frac{x}{(x+5)}[/tex]
= [tex]\frac{6(x+5)+(x+8)}{(x+8)(x+5)}[/tex]
= [tex]\frac{6x+30+x+8}{(x+8)(x+5)}[/tex]
= [tex]\frac{7x+38}{(x+8)(x+5)}[/tex] units
Therefore, perimeter of the given triangle is [tex]\frac{7x+38}{(x+8)(x+5)}[/tex] units
1. Sum of two numbers = 15
Difference of the numbers = 3
Find the numbers.
What is their product?
Answers
So the product is 54 and the two numbers we had to find are 9 and 6.
solve for x. ax-bx=k
Answers
Answer:
x= k/a-b
Step-by-step explanation:
Move all terms to the left side and set equal to zero as well as each factor.
Hope this helps.
The value of x is k/ (a-b).
What is Algebra?algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. it involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
Given:
ax-bx=k
x(a-b)=k
x= k/ (a-b)
Hence, the value x is k/(a-b)
Learn more about algebra here:
https://brainly.com/question/24875240
#SPJ2
Express in simplest form: 12 (2 + ) − (4 + )
Answers
Answer:
20
Step-by-step explanation:
12 (2 + ) − (4 + )
24-4
=20
Answer:
20
Step-by-step explanation:
Round to the number of decimal places stated in bracket.
2.374 [2]
Answers
Answer:
2.37
I hope this helps, also next time make sure your question makes sense
Find all points on the curve x=4cos(t),y=4sin(t) that have the slope of 12.
Answers
Answer:
[tex]\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )[/tex].
Step-by-step explanation:
We need to find all the points on the curve x=4cos(t),y=4sin(t) that have the slope of 1/2.
[tex]x=4cos (t)[/tex]
[tex]\dfrac{dx}{dt}=-4sin (t)[/tex]
[tex]y=4sin (t)[/tex]
[tex]\dfrac{dy}{dt}=4cos (t)[/tex]
Now,
[tex]\dfrac{dy}{dx}=\dfrac{dy}{dt}\times \dfrac{dt}{dx}[/tex]
[tex]\dfrac{dy}{dx}=4cos (t)\times \dfrac{1}{-4sin (t)}[/tex]
[tex]\dfrac{dy}{dx}=-\cot t[/tex]
So, slope of the curve is [tex]-\cot t[/tex].
[tex]-\cot t=\dfrac{1}{2}[/tex]
[tex]-\tan t=2[/tex]
[tex]\tan t=-2[/tex] ...(1)
Using [tex]\sec^2t=1+\tan^2t[/tex], we get
[tex]\sec^2t=1+(-2)^2[/tex]
[tex]\sec^2t=1+4[/tex]
[tex]\sec t=\pm \sqrt{5}[/tex]
[tex]\cos t=\pm \dfrac{1}{\sqrt{5}}[/tex]
Now,
[tex]\sin^2t=1-cos^2t[/tex]
[tex]\sin t=\pm \sqrt{1-\dfrac{1}{5}}[/tex]
[tex]\sin t=\pm \sqrt{\dfrac{4}{5}}[/tex]
[tex]\sin t=\pm \dfrac{2}{\sqrt{5}}[/tex]
It equation (1), tan(t) is negative. So, sin and cos have different signs.
If [tex]\sin t= \dfrac{2}{\sqrt{5}}[/tex], then [tex]\cos t=- \dfrac{1}{\sqrt{5}}[/tex].
[tex]x=4cos (t)=-\dfrac{4}{\sqrt{5}}[/tex]
[tex]y=4sin (t)=\dfrac{8}{\sqrt{5}}[/tex]
If [tex]\sin t=- \dfrac{2}{\sqrt{5}}[/tex], then [tex]\cos t= \dfrac{1}{\sqrt{5}}[/tex].
[tex]x=4cos (t)=\dfrac{4}{\sqrt{5}}[/tex]
[tex]y=4sin (t)=-\dfrac{8}{\sqrt{5}}[/tex]
Therefore, the two points are [tex]\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )[/tex].
8+1/2(12)=x
Solve please
Answers
Answer
14
you have to simplify
8+1/2(12)
14
9/24 =0.375
60% of a class studied for the quiz. 70% of the class passed the quiz. If 12 people did not study for the quiz, how many students passed the quiz
Answers
Answer:
21
Step-by-step explanation:
Answer:
21
Step-by-step explanation:
are intersecting lines always coplanar
Answers
Answer:
yes
Step-by-step explanation:
math 3- Piecewise defined function
Answers
Step-by-step explanation:
A piecewise function is a function built from pieces of different functions over different intervals. For example, we can make a piecewise function f(x) where f(x) = -9 when -9 < x ≤ -5, f(x) = 6 when -5 < x ≤ -1, and f(x) = -7 when -1 <x ≤ 9.
COMBINING LIKE TERMS: Challenge 7 – 3ab + 2a + 6ab + 5 – 4a + 3a – ab
Answers
Answer:
Hope this helps;))
Step-by-step explanation:
-3ab+6ab=3ab
2a-4a+3a=1a
7+5=12
12+3ab+1a
Answer:
-2+2ab-a
Step-by-step explanation:
Never combine unlike terms
Ex. Never combine a and ab
By following those rules, you will get -2+2ab-a as your answer.
Whats value of x is in the solution set of 2(3x-1)>4x-6 A.-10 B.-5 C.-3 D-1
Answers
Answer:
B. -5
Step-by-step explanation:
3x-1 > 4x-6
+1
3x>4x-5
-4x
-x>-5
/-1 /-1
x>-5
Find the length of DE if D is between points C and E, CD = 6.5 cm and CE = 13.8 cm
Answers
Answer:
DE= 7.3
Step-by-step explanation:
you subtract the length if CE - CD to get DE
13.8 - 6.5 = 7.3
Convert 6 7/20
into a decimal
Answers
Hey there!
ANSWER: [tex]0.35[/tex]EXPLANATION:[tex]6 \frac{7}{20}[/tex] as a decimal
The percentage for 6 7/20 is 35%. So if that was the percent, then the decimal would be 0.35.
[tex]0.35(ANSWER)[/tex]
Hope this helps!
[tex]\text {-TestedHyperr}[/tex]
Tier: Homework 1
Solve 2(4y - 5) = 14 983
Answers
Answer:
y = 1874.25
Step-by-step explanation:
2(4y - 5) = 14 983
2*4y + 2*-5 = 14983
8y - 10 = 14983
8y = 14983 + 10
8y = 14993
y = 14993/8
y = 1874.25
Answer:
Step-by-step explanation:
2(4y - 5) = 14
8y - 10 = 14
8y = 24
y = 3
order fruits from least to greatest according to the unit prices 0.84, 2.25, 1.17
Answers
Answer:
0.84, 1.17, 2.25
Step-by-step explanation:
Answer:
.84, 1.17, 2.25
Step-by-step explanation:
You can answer this on your own by finding which numbers are farther away from zero. So the farther you get from zero, the more you have.
P + 4 Solve for p
--------- = 5
6
Answers
Answer:
p = 26
Step-by-step explanation:
(p+4)/6 = 5
Multiply each side by 6
(p+4)/6 *6 = 5*6
p+4 = 30
Subtract 4 from each side
p+4-4 = 30-4
p = 26
Under the Declaration of Independence ordinary citizens have the right to do what and why?
Answers
Answer:
yes, ordinary netizens have a right to do what they want or what opinion they want to say. Declaration of Indepence is not just for powerful people but also for ordinary netizens in order for them to spek the truth