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
Vitek1552 [10]
3 years ago
10

Simplify cotø(tanø+cotø)​

Mathematics
1 answer:
Sladkaya [172]3 years ago
4 0

Answer:

\large\boxed{\cot\theta(\tan\theta+\cot\theta)=1+\cot^2\theta=\dfrac{1}{\sin^2\theta}=\csc^2\theta}

Step-by-step explanation:

\text{Use}\\\\\text{distributive property:}\ a(b+c)=ab+ac\\\cot\alpha\tan\alpha=1.\\\\======================\\\\\cot\theta(\tan\theta+\cot\theta)=(\cot\theta)(\tan\theta)+(\cot\theta)(\cot\theta)\\\\=1+\cot^2\theta\\\\\text{If you want next transformation, then use:}\\\\\cot\alpha=\dfrac{\cos\alpha}{\sin\alpha}\\\\\sin^2\alpha+\cos^2\alpha=1\\\\=======================

=1+\left(\dfrac{\cos\theta}{\sin\theta}\right)^2=1+\dfrac{\cos^2\theta}{\sin^2\theta}=\dfrac{\sin^2\theta}{\sin^2\theta}+\dfrac{\cos^2\theta}{\sin^2\theta}=\dfrac{\sin^2\theta+\cos^2\theta}{\sin^2\theta}\\\\=\dfrac{1}{\sin^2\theta}\\\\\text{If you want next transformation, then use:}\\\\\csc\alpha=\dfrac{1}{\sin\alpha}\\\\=\left(\dfrac{1}{\sin\theta}\right)^2=(\csc\theta)^2=\csc^2\theta

You might be interested in
HELP ASAP PLS I NEED HELP
Alexus [3.1K]

Answer:

B

Step-by-step explanation:

r^2 is 0.9997, and after 10 years it'll be 95660

3 0
3 years ago
How many 1/8-inch pieces of ribbon can be cut from a piece of ribbon that is 3/4 inch long? It can't be a fraction, sadly :')
SIZIF [17.4K]

Answer:

6 pieces.

Step-by-step explanation:

3/4 divided by 1/8

= 3/4 / 1/8        

Invert the 1/8 and multiply:

= 3/4 * 8/1

= 24/4

= 6.

7 0
3 years ago
Read 2 more answers
There are two numbers whose sum is 64. The larger number subtracted from 4 times the smaller number gives 31. Find the numbers.
Pani-rosa [81]

There are two numbers whose sum is 64. The larger number subtracted from 4 times the smaller number gives 31. Then the numbers are 45 and 19

<h3><u>Solution:</u></h3>

Given that, There are two numbers whose sum is 64.  

Let the number be a and b in which a is bigger.

Then, a + b = 64 ------ eqn (1)

The larger number subtracted from 4 times the smaller number gives 31.  

4 x b – a = 31  

4b – a = 31 ----- eqn (2)

We have to find the numbers.

So, from eqn (2)

a = 4b – 31

Subatitute a in (1)

4b – 31 + b = 64

On solving we get

5b  = 64 + 31  

5b = 95

b = 19

So, b = 19, then eqn 1

a + 19 = 64

On simplification,

a = 64 – 19

a = 45  

Hence, the two numbers are 45 and 19

3 0
3 years ago
PLZZZZ HELPPPP !!!!!
Irina-Kira [14]
5 to -4 is your answer
3 0
2 years ago
Read 2 more answers
A new iPhone 13 is on sale for $999. You get a 10% discount for being a student. But, you are buying the phone at the Apple Stor
soldier1979 [14.2K]
You would pay $1100.15 (rounded to nearest hundredths)(unrounded would be 1100.14875)
3 0
3 years ago
Other questions:
  • Juan is 3 times as old as Carmen. Together, their ages add up to 24. How old is each person?
    15·2 answers
  • What is x X/5=15. ⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️
    14·2 answers
  • Four hundred nine thousandths in decimal form
    6·1 answer
  • How much money will Rachel have in her account in ten years
    10·1 answer
  • Quadrilateral ABCD is inscribed in this circle. What is the measure of angle c?
    14·1 answer
  • If f (x) = StartRoot one-half x minus 10 EndRoot + 3, which inequality can be used to find the domain of f(x)?
    9·2 answers
  • there are 30 students in a class. five of them are randomly selected to form a dance comittee how many different comittees can b
    10·2 answers
  • In triangle def the measure of angle F=90 degrees fe=21 df=20cand ed=29 what is the cosine of angle e to nearest hundredth
    8·1 answer
  • X + 5 is a factor of f(x) = x ^ 3 - 2x ^ 2 - 23x + 60 to factor f(x) completely.
    10·1 answer
  • What is the property of 8+(-8)=8?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!