1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
fomenos
3 years ago
8

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

Mathematics
1 answer:
BlackZzzverrR [31]3 years ago
7 0
We will start off working on the right hand side. 
<span>cot x - tan x </span>
<span>= [cos x / sin x] - [sin x / cos x] </span>
<span>= [(cos x)^ 2 - (sin x)^2] / [sin x cos x] </span>

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

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

<span>Hence, we will get: </span>
<span>[(cos x)^ 2 - (sin x)^2] / [sin x cos x] </span>
<span>= [cos 2x] / (1/2)[sin 2x] </span>
<span>= 2[cos 2x] / [sin 2x] </span>
<span>= 2cot 2x </span>
You might be interested in
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

3 0
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.

7 0
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:

  • brainly.com/question/12943520
  • brainly.com/question/12960754

#LearnwithBrainly

7 0
3 years ago
Other questions:
  • Given line has the equation 2X +12 Y equals negative one what is the equation in slope intercept form of the line that is perpen
    14·2 answers
  • (17 POINTS) Solve the following equation. 3(y-5) +2 = 5
    6·2 answers
  • Which of the fallowing best completes the sequence below???
    8·2 answers
  • -4(-11+4n) -3( -2n+9)
    12·2 answers
  • Determine the range of the function.
    15·1 answer
  • Sal bought a house for $78,524.60. Twelve years later he sold the house for 2 3/4 times as much. What was the sale price of the
    15·1 answer
  • Which expression represents a number that is one fourth as great. as 10-2?
    5·1 answer
  • The weight of an object on the moon is 1/6 it's weight on Earth. Write 1/6 as a decimal.
    15·1 answer
  • Find the total surface area of the following prism.
    14·1 answer
  • Given f(x) = 7 - 4x. If the domain of the function is {-4, 0, 1.75, 3}, what is the range of the function?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!