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
Oliga [24]
3 years ago
13

Prove that, tan θ ( 1 + cot ^ 2 θ ) / ( 1 + tan ^ 2 θ ) = cot θ

Mathematics
1 answer:
Gekata [30.6K]3 years ago
3 0

Answer:

(identity has been verified)

Step-by-step explanation:

Verify the following identity:

tan(θ) (cot(θ)^2 + 1)/(tan(θ)^2 + 1) = cot(θ)

Multiply both sides by tan(θ)^2 + 1:

tan(θ) (cot(θ)^2 + 1) = ^?cot(θ) (tan(θ)^2 + 1)

(cot(θ)^2 + 1) tan(θ) = tan(θ) + cot(θ)^2 tan(θ):

tan(θ) + cot(θ)^2 tan(θ) = ^?cot(θ) (tan(θ)^2 + 1)

cot(θ) (tan(θ)^2 + 1) = cot(θ) + cot(θ) tan(θ)^2:

tan(θ) + cot(θ)^2 tan(θ) = ^?cot(θ) + cot(θ) tan(θ)^2

Write cotangent as cosine/sine and tangent as sine/cosine:

sin(θ)/cos(θ) + sin(θ)/cos(θ) (cos(θ)/sin(θ))^2 = ^?cos(θ)/sin(θ) + cos(θ)/sin(θ) (sin(θ)/cos(θ))^2

(sin(θ)/cos(θ)) + (cos(θ)/sin(θ))^2 (sin(θ)/cos(θ)) = cos(θ)/sin(θ) + sin(θ)/cos(θ):

cos(θ)/sin(θ) + sin(θ)/cos(θ) = ^?(cos(θ)/sin(θ)) + (cos(θ)/sin(θ)) (sin(θ)/cos(θ))^2

(cos(θ)/sin(θ)) + (cos(θ)/sin(θ)) (sin(θ)/cos(θ))^2 = cos(θ)/sin(θ) + sin(θ)/cos(θ):

cos(θ)/sin(θ) + sin(θ)/cos(θ) = ^?cos(θ)/sin(θ) + sin(θ)/cos(θ)

The left hand side and right hand side are identical:

Answer: (identity has been verified)

You might be interested in
Help with 4 and 5 please!!
Ghella [55]
Question 4
The magnitude;
Using Pythagoras theorem,
 (-200)² + (-530)² = 320900
                 Length = √320900
                              =  566.5 mi
To get the angle
Tan θ = opposite/adjacent
          = 200/530
          =  0.3774
       θ = tan^-1 (0.3774)
          =  20.67
          ≈ 21°
The direction from the Cartesian plane is south of west.
Therefore, the magnitude and the direction will be;
 About 566.5 mi, 21° south of west

Question 5.
To get the resultant of two vectors we just add the two vectors given.
This involves adding the corresponding values.
Thus, for <-6,5> and <6,-5>
Resultant vector = <(-6+6),(5+-5>
                           = <0,0>
 
4 0
3 years ago
One out of 23 high school ball players plays college ball. One out of 35 college players plays professional ball. What fraction
Gnoma [55]

Answer:

\frac{35}{23} is the required fraction.

Step-by-step explanation:

We have  been given  that  23 high school ball players plays college ball.

And 35 college players plays professional ball  

So we need to find fraction of high school players professional ball

\frac{35}{23} is the required fraction.


6 0
3 years ago
20 points !!! -3/8x-20+2x&gt;6
Semenov [28]

Answer:

x > 16

Step-by-step explanation:

- \frac{3}{8} x -20+2x>6

Add 20 to both sides:

-  \frac{3}{8} x + 2x > 26

Multiply 8 on both sides:

- 3x + 16x > 208

13x > 208

Divide by 13 on both sides:

x > 16

3 0
3 years ago
Read 2 more answers
6. a semicircle has as its diameter the hypotenuse of a right triangle shown below. determine the area of the semicircle to the
jeyben [28]

Answer:

A = 137.3cm^2

Step-by-step explanation:

Given

See attachment

Required

The area of the semicircle

First, we calculate the hypotenuse (h) of the triangle

Considering only the triangle, we have:

\cos(68) = \frac{7}{h} --- cosine formula

Make h the subject

h = \frac{7}{\cos(68)}

h = \frac{7}{0.3746}

h = 18.7

The area of the semicircle is then calculated as:

A = \frac{\pi h^2}{8}

This gives:

A = \frac{3.14 * 18.7^2}{8}

A = \frac{1098.03}{8}

A = 137.3cm^2

7 0
3 years ago
A gallon of apple juice is $7.A pack of eight 4.23 oz box apple juice is 2.39.Which is a better deal?
VikaD [51]
128 ounces in a gallon
The pack is 33.84 ounces in total

gallon for 7=18 cents per ounce
pack for 2.39 is .07 cents per ounce

So the pack is a better deal
4 0
3 years ago
Read 2 more answers
Other questions:
  • Mary is five times older than Julian. If the<br> sum of their ages is 42, how old is Mary?
    6·2 answers
  • 13. On a trip of 525 miles, how many minutes faster is it to travel at 60 miles per hour than
    13·1 answer
  • Write four solution of the equation=2x+y=7​
    6·1 answer
  • What is the value of 4x to the third +4x if x is 4
    13·1 answer
  • What is 576 divided by 47
    15·1 answer
  • 00:00
    13·1 answer
  • Solve for x and y 4x, 15 X + 12, 3y<br>(it's for a parallelogram)​
    7·1 answer
  • What operation on both sides of the equation 6x=42 isolates the variable on one side? There may be more than one correct answer.
    11·2 answers
  • A 5 person sports team has an average 40 yard dash time of 5. 7 seconds. When a 6th player is added to the team, the new mean is
    11·1 answer
  • If 750 was 1, then 301 would be?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!