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
MariettaO [177]
2 years ago
6

How can csc^2-cot^2 = 1?

Mathematics
1 answer:
Softa [21]2 years ago
6 0

ANSWER

By simplifying the left hand side using the Pythagorean Identity.

EXPLANATION

The given identity is

\csc^{2} (x) -  \cot^{2} (x) = 1

Take the left hand side and simplify to get the right hand side.

\csc^{2} (x) -  \cot^{2} (x) =  \frac{1}{\sin^{2} (x)}  - \frac{ \cos^{2} (x)}{\sin^{2} (x)}

Collect LCM for the denominators.

\csc^{2} (x) -  \cot^{2} (x) =  \frac{1 -  \cos^{2} (x)}{\sin^{2} (x)}

Recall the Pythagorean Identity.

\cos^{2} (x) +  \sin^{2} (x) = 1

This implies that:

1 -  \cos^{2} (x) =  \sin^{2} (x)

We substitute this to get,

\csc^{2} (x) -  \cot^{2} (x) =  \frac{\sin^{2} (x)}{\sin^{2} (x)}

\csc^{2} (x) -  \cot^{2} (x) = 1

You might be interested in
A=8b+c solve for b <br> Please help!
balu736 [363]

Answer:

(A-c)/8 = b

Step-by-step explanation:

A = 8b +c

A - c = b

(A-c)/8 = b

Hope this helps you!

3 0
3 years ago
Whats the distance between coordinates (-6,8) and (-6,-3)
insens350 [35]

Answer:

there away from eachother for 5 spaces.

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
During a semester, a student received scores of 76, 80, 83,
Fantom [35]
Add all those numbers and divide by 6 will get you 78
5 0
2 years ago
It’s My Final Test I’m not sure what the answer is
Elena-2011 [213]

Answer:

D

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Solve for c.
Mrrafil [7]

<u>Answer:</u>

The answer is c = \frac{d+ab}{a}

<u>Solution:</u>

When a sum of two numbers is multiplied by a number, the number can be distributed to the addends separately, then adding the products together will produce the same result as multiplying sum by the number. This property is called distributive property of multiplication.

To find the value of, a(c-b)=d

On applying the distributive property of multiplication which is [a\times(b+c)=a\times b+a\times c]

Here we get,

a\times(c-b)=a\times c-a\times b

So the equation will be,

a\times c-a\times b=d

ac-ab=d

ac=d+ab

c=\frac{d+ab}{a} or \frac{d}a+\frac{ab}{a}

7 0
2 years ago
Read 2 more answers
Other questions:
  • Original: 379 New: 83
    9·1 answer
  • What’s 5/6 divided by 5/2 in fraction form
    12·2 answers
  • Movies are on sale for 3/
    15·2 answers
  • 8.45 as a mixed number
    10·1 answer
  • Parker baked 80 cookies for a bake sale. At the bake sale, 70% of his cookies sold. How many of Parker’s cookies were sold?
    10·2 answers
  • How many solutions does the system have?
    7·2 answers
  • Which of the following is equal to 19.4?
    13·1 answer
  • What is 64 thousandths in decimal form​
    8·2 answers
  • Hamal has a new part time job bagging groceries after school. The equation y=10x+50 show the relationship between his hours of w
    9·2 answers
  • Hi, Could anyone help me with my homework
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!