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3 years ago

How do I prove that 2 cot 2x = cot x-tan x?

1 answer:

7 0

We will start off working on the right hand side.
cot x - tan x 
= [cos x / sin x] - [sin x / cos x] 
= [(cos x)^ 2 - (sin x)^2] / [sin x cos x] 

This is where it gets a bit tougher if you do not have your formula list with you. 
(cos x)^ 2 - (sin x)^2 = cos(2x) 
sin 2x = 2 sin x cos x 

Note that by arranging the second formula, we will have sin x cos x = (1/2) sin 2x 

Hence, we will get: 
[(cos x)^ 2 - (sin x)^2] / [sin x cos x] 
= [cos 2x] / (1/2)[sin 2x] 
= 2[cos 2x] / [sin 2x] 
= 2cot 2x

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A company claims that 5% of its products will be defective. A simple random sample of 300 products contain 10 defective products

Radda [10]

Answer:

wateva

Step-by-step explanation:

wateva u want it too be good luck

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3 years ago

Find the equation of line b described below, in slope-intercept form

Serjik [45]

Given:

Line a is perpendicular to line b .

Line a passes through the points (1,-8) and (9,-12) .

Line b passes through the point (-8, -16).

To find:

The equation of b.

Solution:

Line a passes through the points (1,-8) and (9,-12) . So, slope of line a is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m_a=\dfrac{-12-(-8)}{9-1}$

$m_a=\dfrac{-12+8}{8}$

$m_a=\dfrac{-4}{8}$

$m_a=-\dfrac{1}{2}$

Product of slopes of two perpendicular lines is -1.

$m_a\times a_b=-1$

$-\dfrac{1}{2}\times a_b=-1$

$b=2$

Slope of line b is 2.

If a line passing through a point $(x_1,y_1)$ with slope m, then equation of line is

$y-y_1=m(x-x_1)$

Line b passing through (-8,-16) with slope 2. So, equation of line b is

$y-(-16)=2(x-(-8))$

$y+16=2(x+8)$

$y+16=2x+16$

Subtract 16 from both sides.

$y=2x$

Therefore, the equation of line b is $y=2x$ .

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3 years ago

11. Higher Order Thinking Using what you know

Lynna [10]

Answer:

m∠1 + m∠3 = m∠2 + m∠4

Step-by-step explanation:

In the figure attached,

In the given trapezoid if two sides AB and CD are parallel and AD is a transverse,

m∠1 + m∠3 = 180°

Similarly, if AB and CD are parallel and BC is a transverse,

m∠2 + m∠4 = 180°

Therefore, m∠1 + m∠3 = m∠2 + m∠4 is the relation between these angles.

6 0

3 years ago

Use the distributive property to expand the expression (8x + 3y) - (5z + 3)

lord [1]

Answer:

8x+3y-5z-3

Step-by-step explanation:

8x+3y-5z-3

Just multiply the second parenthesis with the minus for your answer.

4 0

3 years ago

Read 2 more answers

The coffee cups can hold 7/9 of a pint of liquid. If Emily puts 2/3 of s pint of coffee into a cup, how much milk can a customer

Bezzdna [24]

1/9 pints of milk can be added by a customer

Step-by-step explanation:

We have to subtract simple fractions to find the amount of milk that can be added to a cup of coffee

Given

Total Capacity of a cup = 7/9 pints

Coffee to be added in a cup = 2/3 pints

So in order to find the amount of milk that can be added we have to subtract the amount of coffee from the total capacity of cup.

So,

$Amount\ of\ milk = \frac{7}{9} - \frac{2}{3}\\=\frac{7-6}{9} = \frac{1}{9}$

Hence,

1/9 pints of milk can be added by a customer

Keywords: Fractions, addition

Learn more about fractions at:

#LearnwithBrainly

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3 years ago