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2 years ago

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Mathematics

1 answer:

ioda2 years ago

3 0

Answer:

Step-by-step explanation:

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Prove that if sin (2 + y) = 3 sin (x - y), then tan x = 2 tany.

nignag [31]

Answer:

The proof is given below.

Step-by-step explanation:

Given: ( the correct question and ans is as follow )

sin (x + y) = 3sin ( x - y)

To Prove

tan x = 2 tan y

Proof:

$\sin (x+y) = 3\sin (x-y)$

Using the identities

$\sin (A+B) = \sin A.\cos B + \cos A.\sin B\\and\\\sin (A-B) = \sin A.\cos B - \cos A.\sin B\\$

we get

$\sin x.\cos y + \cos x.\sin y = 3(\sin x.\cos y - \cos x.\sin y)\\\sin x.\cos y + \cos x.\sin y = 3\sin x.\cos y - 3\cos x.\sin y$

Now we will take sin x . cos y to the left hand side and cos x . sin y to the right hand side,we get

$3\sin x.\cos y - \sin x.\cos y = 3\cos x.\sin y +\cos x.\sin y\\2\sin x.\cos y =4\cos x.\sin y\\\sin x.\cos y =2\cos x.\sin y \ \textrm{4 divide by 2}\\ \frac{\sin x}{\cos x} =2\times \frac{\sin y}{\cos y} \\\textrm{we know identity }\\\frac{\sin x}{\cos x} = \tan x\\\frac{\sin y}{\cos y} = \tan y\\\therefore \tan x = 2\tan y\ ...............{PROVED}$

7 0

3 years ago

Alladin's Amusement Park has a popular roller coaster ride. There are 2 trains. Each train has 7 cars. Each car holds 16 people.

Nataly [62]

Answer:

224

Step-by-step explanation:

Number of trains in the roller coaster = 2

Number cars in each train = 7

Total number of cars = Number of trains $\times$ Number of cars in each train = $7\times 2$ = 14

Number of people in each car = 16

Total number of people in 14 cars = Number of people in one car $\times$ Number of cars = 16 $\times$ 14 = 224

i.e.

Total number of people in the roller coaster in one run = 224

Number of runs made by each train in one hour = 10

Therefore, Total number of people that can ride the roller coaster in one hour can be found by multiplying the number of runs with total number of people in the roller coaster in one run.

224 $\times$ 10 = <em>2240</em>

4 0

2 years ago

Gennadij [26K]

The common ratio is 5 because each number is being multiplied/divided by 5

6 0

2 years ago

What is the GCF of the expression 5x2y + 10xy2?

DerKrebs [107]

Answer:

$5xy$