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
PSYCHO15rus [73]
3 years ago
14

Tan^2 A/1+cot^2 A + cot^2 A/1+tan^2 A=sec^2 A cosec^2 A-3

Mathematics
1 answer:
omeli [17]3 years ago
3 0
\frac{tan^2x}{1+cot^2x}+\frac{cot^2x}{1+tan^2x}=sec^2x\ cosec^2x-3\\\\L=\frac{tan^2x(1+tan^2x)+cot^2x(1+cot^2x)}{(1+cot^2x)(1+tan^2x)}=\frac{tan^2x+tan^4x+cot^2x+cot^4x}{1+tan^2x+cot^2x+tanxcotx}\\\\=\frac{tan^2x+cot^2x+tan^4x+cot^4x}{1+tan^2x+cot^2x+1}=\frac{tan^2x+2+cot^2x+tan^4x-2+cot^4x}{tan^2x+cot^2x+2}

=\frac{(tanx+cotx)^2+(tan^2x-cot^2x)^2}{(tanx+cotx)^2}=\frac{(tanx+cotx)^2}{(tanx+cotx)^2}+\frac{(tan^2x-cot^2x)^2}{(tanx+cotx)^2}\\\\=1+\frac{(tanx-cotx)^2(tanx+cotx)^2}{(tanx+cotx)^2}=1+(tanx-cotx)^2\\\\=1+tan^2x-2tanx\ cotx+cot^2x=tan^2x+cot^2x+1-2\\\\=\left(\frac{sinx}{cosx}\right)^2+\left(\frac{cosx}{sinx}\right)^2-1=\frac{sin^2x}{cos^2x}+\frac{cos^2x}{sin^2x}-1=\frac{sin^4x+cos^4x}{sin^2x\ cos^2x}-1

=\frac{(sin^2x)^2+2sin^2x\ cos^2x+(cos^2x)^2-2sin^2x\ cos^2x}{sin^2x\ cos^2x}-1\\\\=\frac{(sin^2x+cos^2x)^2-2sin^2x\ cos^2x}{sin^2x\ cos^2x}-1=\frac{1^2-2sin^2x\ cos^2x}{sin^2x\ cos^2x}-1\\\\=\frac{1}{sin^2x\ cos^2x}-\frac{2sin^2x\ cos^2x}{sin^2x\ cos^2x}-1=\frac{1}{sin^2x}\cdot\frac{1}{cos^2x}-2-1\\\\=cosec^2x\cdot sec^2x-3=sec^2x\ cosec^2x-3=R
You might be interested in
Image attached down bellow
rusak2 [61]

Answer:

C

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
This question has been difficult for me
olchik [2.2K]
So the area of a circle is πr²

if the diameter of the sign 30 in then the radius is 15 in

Now Area of Circle = π(15 in)²
                               
                              =  706.86

Thus by estimation the best answer is OPTION C
7 0
3 years ago
Which inequality is the same as 7-2/b <5/b
ale4655 [162]

Answer: b

7(b-1)/b less than or equal to 0

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
6b 4r represents the total cost of the rice and beans Gabriel bought. If he returns 2 bags of beans and 1 bag of rice, the expre
Julli [10]

The total cost of rice and beans bought by Gabriel is 6b + 4r.

The simplified expression of the final cost is 4b + 3r.

<h3>What is simplification?</h3>

Simplification can be defined as a process of replacing a mathematical expression by the cancellation of common factors, regrouping of terms in the same variable to get the more simple form of the given expression.

Given that

6b + 4r represents the total cost of the rice and beans Gabriel bought.

He returns 2 bags of beans and 1 bag of rice.

This can be written as,

\rm 2b+1r

Then, the total number of bags of rice and beans is given as,

\rm (6b+4r)- (\rm 2b+1r)

When we simplify the above equation, we get,

\rm (6b+4r)- (\rm 2b+1r)\\\\6b+4r-2b-1r\\\\4r+3r

Hence we can conclude that the expression for rice and beans after the return is (4b+3r).

To know more about simplification, follow the link given below.

brainly.com/question/12616840.

8 0
2 years ago
I only need help on number 6 plzzzz help
Gennadij [26K]
That question is asking for the time so your answer will specifically be in hours. And I'm not sure if you divide or you multiply but I'm pretty sure the correct answer is dividing because tomorrow so cancel the miles they will be left with hours. I don't know if that makes sense to you but it kind of makes sense to me somehow.
4 0
3 years ago
Read 2 more answers
Other questions:
  • The answer to this (C=20+10h) which describes the. cost (c) of renting a canoe, in dollars, as a function of the number hours (h
    13·1 answer
  • X +10=14 &lt;--how does one solve this?​
    8·1 answer
  • The world record in the long jump is 29 feet and 4 1/2 inches. how many inches short of 10 yards is the record long jump?
    15·1 answer
  • Two number cubes each with the numbers 1-6 are rolled what is the probability that the sum of the rolled numbers is 2?
    10·1 answer
  • Write a polynomial of least degree with rational coefficients and with the root 3-2 square root of 7
    14·1 answer
  • Convert 8 1/4% to a decimal
    10·2 answers
  • You might need:
    13·1 answer
  • I have no clue how to do this. For my equations i got
    5·1 answer
  • LOTS OF POINTS!! WILL GIVE BRAINLIEST!! HELP!!!!!!!!!! answer the question below.
    14·2 answers
  • This dot plot is not symmetric, and the data set has two
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!