MATHEMATICS HIGH SCHOOL

Please someone help me to prove this.

Answers

Answer 1

Answer:

Answer: see proof below

Step-by-step explanation:

Use the Power Reducing Identity: sin² Ф = (1 - cos 2Ф)/2

Use the Double Angle Identity: sin 2Ф = 2 sin Ф · cos Ф

Use the following Sum to Product Identities:

$\sin x - \sin y = 2\cos \bigg((x+y)/(2)\bigg)\sin \bigg((x-y)/(2)\bigg)\n\n\n\cos x - \cos y = -2\sin \bigg((x+y)/(2)\bigg)\sin \bigg((x-y)/(2)\bigg)$

Proof LHS → RHS

$\text{LHS:}\qquad \qquad \qquad (\sin^2A-\sin^2B)/(\sin A\cos A-\sin B \cos B)$

$\text{Power Reducing:}\qquad (\bigg((1-\cos 2A)/(2)\bigg)-\bigg((1-\cos 2B)/(2)\bigg))/(\sin A \cos A-\sin B\cos B)$

$\text{Half-Angle:}\qquad \qquad (\bigg((1-\cos 2A)/(2)\bigg)-\bigg((1-\cos 2B)/(2)\bigg))/((1)/(2)\bigg(\sin 2A-\sin 2B\bigg))$

$\text{Simplify:}\qquad \qquad (1-\cos 2A-1+\cos 2B)/(\sin 2A-\sin 2B)\n\n\n.\qquad \qquad \qquad =(-\cos 2A+\cos 2B)/(\sin 2A - \sin 2B)\n\n\n.\qquad \qquad \qquad =(\cos 2B-\cos 2A)/(\sin 2A-\sin 2B)$

$\text{Sum to Product:}\qquad \qquad (-2\sin \bigg((2B+2A)/(2)\bigg)\sin \bigg((2B-2A)/(2)\bigg))/(2\cos \bigg((2A+2B)/(2)\bigg)\sin \bigg((2A-2B)/(2)\bigg))$

$\text{Simplify:}\qquad \qquad (-2\sin (A + B)\cdot \sin (-[A - B]))/(2\cos (A + B) \cdot \sin (A - B))$

$\text{Co-function:}\qquad \qquad (2\sin (A + B)\cdot \sin (A - B))/(2\cos (A + B) \cdot \sin (A - B))$

$\text{Simplify:}\qquad \qquad \quad (\cos (A+B))/(\sin (A+B))\n\n\n.\qquad \qquad \qquad \quad =\tan (A+B)$

LHS = RHS: tan (A + B) = tan (A + B) $\checkmark$

Answer 2

Answer:

We know that,

$\dag\bf\:sin^2A=(1-cos2A)/(2)$

$\dag\bf\:sin2A=2sinA\:cosA$

___________________________________

Now, Let's solve !

$\leadsto\:\bf(sin^2A-sin^2B)/(sinA\:cosA-sinB\:cosB)$

$\leadsto\:\sf((1-cos2A)/(2)-(1-cos2B)/(2))/((2sinA\:cosA)/(2)-(2sinB\:cosB)/(2))$

$\leadsto\:\sf(1-cos2A-1+cos2B)/(sin2A-sin2B)$

$\leadsto\:\sf(2sin(2A+2B)/(2)\:sin(2A-2B)/(2))/(2sin(2A-2B)/(2)\:cos(2A+2B)/(2))$

$\leadsto\:\sf(sin(A+B))/(cos(A+B))$

$\leadsto\:\bf{tan(A+B)}$

Related Questions

Brad can make 4 key chains in an hour. Velma can make only 3 key chains in an hour, but she already has 6 completed key chains. How can Brad use a system of equations to determine when he will have the same number of key chains as Velma?
You pick a card at random. Without putting the first card back, you pick a second card at random. [1] [2] [3] What is P(3, greater than 2)? Write your answer as a percentage.
Jabari owns 100 shares of Stock A and 45 shares of Stock B. For the past month, his stocks have been fluctuating inversely each week. Stock A decreased by m cents per share and Stock B increased by n cents per share. Which equation can be used to find the total change in value of Jabari's shares?
How do you rename each additive inverse without parentheses -(2x+7)
In a binary tree, what is denoted by "h(t)"? A) Height of the tree B) Root of the tree C) Neighbors of the root D) Binary value of the tree

PLS HELP FIRST CORRECT ANSWER GETS BRAINLIEST !! A pile of tailings from a gold dredge is in the shape of a cone. The diameter of the base is 34 feet and the height is 16 feet. Approximately, how many cubic feet of gravel is in the pile? Use π = 3.14.A. 14,527 ft³
B. 285 ft³
C. 4,840 ft³
D. 6,032 ft³

Answers

The volume of the cone is 4840 cubic ft if the diameter of the base is 34 feet and the height is 16 feet option (C) is correct.

What is a cone?

It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.

$\rm V=\pi r^2(h)/(3)$

Volume can be defined as a three-dimensional space enclosed by an object or thing.

It is given that:

A pile of tailings from a gold dredge is in the shape of a cone.

The diameter of the base is 34 feet and the height is 16 feet.

As we know,

The volume of the cone is given by:

$\rm V=\pi r^2(h)/(3)$

r = 34/2 = 17 ft

h = 16 feet

Plug the above values in the formula:

$\rm V=\pi (17)^2(16)/(3)$

After solving:

V = 1541.33π cubic feet

Take π = 3.14

V = 1541.33(3.14) cubic feet

V = 4839.78 ≈ 4840 cubic ft

Thus, the volume of the cone is 4840 cubic ft if the diameter of the base is 34 feet and the height is 16 feet option (C) is correct.

Learn more about the cone here:

brainly.com/question/16394302

#SPJ5

Answer:

C: $V=4840 (2 s.f.)$

Step-by-step explanation:

The formula for the volume of a cone is:

$V= (1)/(3) \pi r^2h$

Therefore,

$V=(1)/(3)* 3.14*((34)/(2))^2* 16\n\nV=4840 (2 s.f.)$

A coin bank contains twice as many nickels as dimes and five times as many pennies as dimes. The value of the collection is $2.00 or 200cents. How many pennies, nickels,and dimes are in the collection?

Answers

n=number of nickles
d=number of dimes
p=number of pennies

so we have
"twice as many nickles as dimes"
n=2d
"five times as many pennies as dimes"
p=5d

we know that the total value is 200 cents

value=5n+10d+1p
200=5n+10d+p

we know that
n=2d
p=5d
sub those for n and p
200=5(2d)+10d+5d
200=10d+10d+5d
200=25d
divide both sides by 25
8=d
there are 8 dimes

easy, sub
n=2d
n=2(8)
n=16
16 nickles

p=5d
p=5(8)
P=40
40 pennies

40 pennies
16 nicles
8 dimes

An item is priced at $13.37. If the sales tax is 4%, what does the item cost including sales tax?A. $13.90
B. $0.53
C. $18.72
D. $27.27

Answers

4% = 0.04

$13.37x0.04= $0.53

13.37=0.53= $13.90

the answer is A.

What happens when an object accelerates ?

Answers

When an object start to accelerates it changes its state of motion.

How do you find the circumference when you ONLY know the area?

Answers

It's easy if you remember the formulas you learned for the area, diameter,
and circumference of a circle:

-- Area = (pi) (radius)²
-- Diameter = (2) (radius)
-- Circumference = (pi) (diameter)

You know the area. So let's use the first formula to find the circle's radius.

Area = (pi) (radius)²

Divide each side by (pi): Area/pi = (radius)²

Radius = √(area/pi)

Now use the second formula to find the circle's diameter:

Diameter = (2) (radius)

Diameter = 2 √(area/pi)

Now use the third formula to find the circle's circumference:

Circumference = (pi) (diameter)

Circumference = (pi) (2) √(area/pi)

With just a little tweak, that can be written slightly more simply:

Circumference = 2 √(pi x area)

See ? Just the three circle formulas,and a lot of massaging.

What can a doctor use to determine a patient's body fat percentage?Bioelectrical impedance machine
MRI machine
Waist measurement
Weight measurement