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
Ghella [55]
3 years ago
11

Simplify the expression. Quantity cosecant of x to the power of two times secant of x to the power of two divided by quantity se

cant of x to the power of two plus cosecant of x to the power of two.
A. sin^2x
B. cos^2x
C. -1
D. 1
Mathematics
1 answer:
Art [367]3 years ago
3 0

Answer:

D. 1

Step-by-step explanation:

We have the expression, \frac{\csc^{2}x\sec^{2}x}{\sec^{2}x+\csc^{2}x}

We get, eliminating the cosecant function,

\frac{\sec^{2}x}{\frac{\sec^{2}x}{\csc^{2}x}+1}

As, sinx is reciprocal of cosecx and cosx is reciprocal of secx,

i.e. \frac{\sec^{2}x}{\frac{\sin^{2}x}{\cos^{2}x}+1}

i.e. \frac{1}{\cos^{2}x}\times \frac{\cos^{2}x}{\sin^{2}x+\cos^{2}x}

Since, we know that, \sin^{2}x+\cos^{2}x=1

Thus,

\frac{1}{\cos^{2}x}\times \frac{\cos^{2}x}{\sin^{2}x+\cos^{2}x}=1

So, after simplifying, we get that the result is 1.

Hence, option D is correct.

You might be interested in
A town's population went from 25,800 to 42,600 in 15 years. What was the percent of changes?
melomori [17]
42,600 - 25,800 = 16800. That is the increase in 15 years.

You then calculate the increase as a percentage of the original population; 25,800.

16,800 / 25,800 * 100 = 65.11%
8 0
3 years ago
What is the value of y when line m is parallel to line n?
kvasek [131]
Angles B and D are supplementary angles, so if B's angle is 30 degrees, then D's angle at y would be 150, since they have to add to 180.
In short, angle y = 150 
6 0
3 years ago
Read 2 more answers
Which sequences are geometric? Check all that apply.
MatroZZZ [7]

Answer:

The geometric sequences are:

16 , -8 , 4 , -2 , 1 ⇒ 2nd

-15 , -18 , -21.6 , -25.92 , -31.104, ........ ⇒ 3rd

625 , 125 , 25 , 5 , 1 , ........ ⇒ 5th

Step-by-step explanation:

In the geometric sequence there is a constant ratio between each two consecutive terms

Let us find which sequence has  a constant ratio between its consecutive terms

-2 , -4 , -6 , -8 , -10

∵ -4 ÷ -2 = 2

∵ -6 ÷ -4 = 1.5

- No constant ratio between the consecutive terms

∴ The sequence is not geometric

16 , -8 , 4 , -2 , 1

∵ -8 ÷ 16 = -0.5

∵ 4 ÷ -8 = -0.5

∵ -2 ÷ 4 = -0.5

∵ 1 ÷ -2 = -0.5

- There is a constant ratio -0.5 between the consecutive terms

∴ The sequence is geometric

-15 , -18 , -21.6 , -25.92 , -31.104, ........

∵ -18 ÷ -15 = 1.2

∵ -21.6 ÷ -18 = 1.2

∵ -25.92 ÷ -21.6 = 1.2

∵ 31.104 ÷ 25.92 = 1.2

- There is a constant ratio 1.2 between the consecutive terms

∴ The sequence is geometric

4 , 10.5 , 17 , 23.5 , 30, ......

∵ 10.5 ÷ 4 = 2.625

∵ 17 ÷ 10.5 = 1.619047619

- No constant ratio between the consecutive terms

∴ The sequence is not geometric

625 , 125 , 25 , 5 , 1 , ........

∵ 125 ÷ 625 = 0.2

∵ 25 ÷ 125 = 0.2

∵ 5 ÷ 25 = 0.2

∵ 1 ÷ 5 = 0.2

- There is a constant ratio 0.2 between the consecutive terms

∴ The sequence is geometric

5 0
3 years ago
What coefficient would you get for the x terms on the right side of 3x+15=2x+10+x+5
Zielflug [23.3K]

Answer:

x=0

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
25-3x=2x help what’s x
Stolb23 [73]

Answer:

x=5

Step-by-step explanation:

add 3x to 2x

25=5x

then divide 25 by 5x

5=x

and flip

x=5

3 0
3 years ago
Other questions:
  • The equation of the graphed line is..... x+......y=4 ANSWER FAST PLZZXZZ FILL IN THE BLANKS (DOTED LINE)
    8·1 answer
  • Q10 - Please help!!! I will give Brainliest!
    8·2 answers
  • I need help on this one thanks!!
    7·1 answer
  • How can bar diagrams be used to model numerical expressions
    7·2 answers
  • Rectangle PQRS is shown with its diagonals, PR and QS. 
    10·2 answers
  • 5/4*6/25+6/5 ill even give brainliest
    13·2 answers
  • Please just help me. I am now having a bad day because of this website and all I'm doing is asking for help, and all my points a
    8·1 answer
  • I need help asap thank you
    8·1 answer
  • Help please !!!!?!!!!
    10·1 answer
  • Please help.a lot of the problems are confusing to me.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!