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
tester [92]
3 years ago
7

Prove: cot(x) sec^4(x) = cot(x) +2tan(x) + tan^3(x)

Mathematics
1 answer:
masha68 [24]3 years ago
8 0
\bf cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}
\qquad\qquad 
sec(\theta)=\cfrac{1}{cos(\theta)}\quad\qquad  1+tan^2(\theta)=sec^2(\theta)\\\\\\
tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}
\qquad \qquad cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}
\\\\
-------------------------------\\\\
cot(x)sec^4(x)=cot(x)+2tan(x)+tan^3(x)\\\\
-------------------------------\\\\

\bf \textit{so, let's do the left-hand-side}\\\\
cot(x)sec^2(x)sec^2(x)\implies cot(x)[1+tan^2(x)][1+tan^2(x)]
\\\\\\
cot(x)[1^2+2tan^2(x)+tan^4(x)]
\\\\\\
cot(x)+2tan^2(x)cot(x)+tan^4(x)cot(x)
\\\\\\
cot(x)+2\cdot \cfrac{sin^2(x)}{cos^2(x)}\cdot \cfrac{cos(x)}{sin(x)}+\cfrac{sin^4(x)}{cos^4(x)}\cdot \cfrac{cos(x)}{sin(x)}
\\\\\\
cot(x)+2\cdot \cfrac{sin(x)}{cos(x)}+\cfrac{sin^3(x)}{cos^3(x)}\implies \boxed{cot(x)+2tan(x)+tan^3(x)}
You might be interested in
3. Will Question 1 be positive or negative?<br> (5 Points)<br> Positive<br> Negative
Ganezh [65]

Answer:

I need to know what question 1 is because we cant figure it out if you don't have 1)

Step-by-step explanation:

Postive

6 0
3 years ago
A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and
vredina [299]

Answer:

2.35%

Step-by-step explanation:

Mean number of months (M) = 39 months

Standard deviation (S) = 10 months

According to the 68-95-99.7 rule, 95% of the data is comprised within two standard deviations of the mean (39-20 to 39+20 months), while 99.7% of the data is comprised within two standard deviations of the mean (39-30 to 39+30 months).

Therefore, the percentage of cars still in service from 59 to 69 months is:

P_{59\ to\ 69}=\frac{P_{9\ to\ 69}-P_{19\ to\ 59}}{2} \\P_{59\ to\ 69}=\frac{99.7-95}{2}\\P_{59\ to\ 69}=2.35\%

The approximate percentage of cars that remain in service between 59 and 69 months is 2.35%.

8 0
3 years ago
I need some help with this​
Contact [7]
The answer for the first one is city c
8 0
3 years ago
Marcus has two salary options for his new job.
Lady bird [3.3K]

Answer:

$125

Step-by-step explanation:

5 0
3 years ago
15,000 blue trout were released into the Meherrin River for a scientific study. The function, f(x) = 15,000( _ 9 8 ) x , represe
Airida [17]

Ask seri she helps with everything

8 0
3 years ago
Other questions:
  • Which expression gives the volume of a sphere with radius 15?
    12·2 answers
  • Consider the following pair of equations:
    14·1 answer
  • Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the z-score for each of the five observations. If required
    8·1 answer
  • Jenny's math grades are 95, 82, 75, 100, 67, 89, 75, 80, 91, and 70. Make a stem and leaf plot for these grades.
    13·2 answers
  • Let g(x)=x-3 and h(x)=x^2+6 find (h o g) (1)
    5·2 answers
  • Beverly has a bag of marbles that weighs 30 grams. She knows that each marble weighs 1.5 grams and the bag weighs 1.5 grams. Whi
    13·1 answer
  • a bag contains blue, green, yellow, and red marbles. The probability of drawing a yellow marble is 3/20. What is the probability
    13·1 answer
  • Find the missing side of the right triangle. Write the value only.
    14·1 answer
  • 53​% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the
    5·1 answer
  • What is something that multiplies everyday
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!