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
Reil [10]
2 years ago
15

Considering only the values of β for which sinβtanβsecβcotβ is defined, which of the following expressions is equivalent to sinβ

tanβsecβcotβ?
Select the correct answer below:

secβcotβ
tanβ
cotβtanβ
tanβcscβsecβ
Mathematics
1 answer:
-Dominant- [34]2 years ago
8 0

Answer:

\tan(\beta)

Step-by-step explanation:

For many of these identities, it is helpful to convert everything to sine and cosine, see what cancels, and then work to build out to something.  If you have options that you're building toward, aim toward one of them.

{\tan(\theta)}={\dfrac{\sin(\theta)}{\cos(\theta)}    and   {\sec(\theta)}={\dfrac{1}{\cos(\theta)}

Recall the following reciprocal identity:

\cot(\theta)=\dfrac{1}{\tan(\theta)}=\dfrac{1}{ \left ( \dfrac{\sin(\theta)}{\cos(\theta)} \right )} =\dfrac{\cos(\theta)}{\sin(\theta)}

So, the original expression can be written in terms of only sines and cosines:

\sin(\beta)\tan(\beta)\sec(\beta)\cot(\beta)

\sin(\beta) * \dfrac{\sin(\beta) }{\cos(\beta) } * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) } {\sin(\beta) }

\sin(\beta) * \dfrac{\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} {\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}

\sin(\beta) *\dfrac{1 }{\cos(\beta) }

\dfrac{\sin(\beta)}{\cos(\beta) }

Working toward one of the answers provided, this is the tangent function.


The one caveat is that the original expression also was undefined for values of beta that caused the sine function to be zero, whereas this simplified function is only undefined for values of beta where the cosine is equal to zero.  However, the questions states that we are only considering values for which the original expression is defined, so, excluding those values of beta, the original expression is equivalent to \tan(\beta).

You might be interested in
Which equation gives the value of the circumference, C, of a circle with a diameter of 56 feet?
Keith_Richards [23]

Answer:175.84 ft

Step-by-step explanation: the equation would be diameter times pi

4 0
3 years ago
What is the logarithmic form of 144=12^2
Aloiza [94]
I beleive 144=2 is the answer.

If you have to divide that to get 1 number it would be 72.


???????????????????????
5 0
3 years ago
Read 2 more answers
Is (0,5) a solution to the equation y=2x?​
klio [65]

Answer:

No.

Step-by-step explanation:

If (0,5) is a solution to y=2x, then 5=2(0) has to be true.

It is not because 5=2(0) is not true.

2(0)=0 and 0 is definitely not 5.

An example of a point on y=2x is (5,10) since 10=2(5) is true.

3 0
3 years ago
Read 2 more answers
Please help! Giveaway soon to celebrate expert level :D
elena-s [515]

Answer:

1 antonym

2 interrogative

3 verb

4 inflection

5 declarative

6 synonym

7 exclamatory

8 pronunciation

9 accent

10 imperative

4 0
3 years ago
Read 2 more answers
Tickets to a show cost $5.50 for adults and $4.25 for students. A family is purchasing 2 adult tickets and 3 student tickets. Wh
MArishka [77]

Answer:

$23.75

........................

8 0
3 years ago
Read 2 more answers
Other questions:
  • Me ajudem nessa equação :<br> 10x - 12 + 10= +18 - 20
    13·1 answer
  • Solve 4(x + 1) = 4x + 4.
    10·2 answers
  • Write the expression that shows 3 times the sixth power of 10.
    13·2 answers
  • Which multiplication property is 6 x 7 = ( 6 x 7) + ( 6 x 2)?
    6·1 answer
  • Dan says 3/5 is the same as 3.5 is he correct?
    7·2 answers
  • Find the product.<br><br> 2a2(5b2+3ab+6a+1)<br><br> PLEASE HELP!!!! ASAP!!!
    9·2 answers
  • Plus answer now Find 3/5 of 3000.
    14·2 answers
  • What are the steps to understanding this problem as well as the answers.
    10·1 answer
  • Cual propiedad de los números reales se ilustra en los siguientes enunciados? 2(13+−8)=26+−16​
    15·1 answer
  • Given y = a(x - h)^2 + k, p = <br> A. a <br> B. 4a <br> C. 1/4a
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!