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3 years ago

What is the slope of a line perpendicular to y=2/3x-2 ?

Mathematics

1 answer:

Margarita [4]3 years ago

3 0

Answer:

Step-by-step explanation:

y=2/3x-2

Negative reciprocal

y=-3/2x-2,

So the answer is -3/2

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3 years ago

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

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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

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

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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

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

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