(3 to the power of 2) + (5 − 2) ⋅ 4 − 6 over 3

Mathematics

2 answers:

Oduvanchick [21]4 years ago

4 0

Do parentheses first: 9+7x4-6/3 then multiplication/division: 9+28-2 then addition/subtraction: =35

matrenka [14]4 years ago

3 0

(3 to the power of 2) + (5 − 2) ⋅ 4 − 6 over 3 =19

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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

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