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
777dan777 [17]
3 years ago
12

Prove that (Root of Sec A - 1 / Root of Sec A + 1) + (Root of Sec A + 1 / Root of Sec A - 1) = 2 cosec A

Mathematics
1 answer:
iVinArrow [24]3 years ago
7 0

Answer:

The answer is below

Step-by-step explanation:

We need to prove that:

(Root of Sec A - 1 / Root of Sec A + 1) + (Root of Sec A + 1 / Root of Sec A - 1) = 2 cosec A.

Firstly, 1 / cos A = sec A, 1 / sin A = cosec A and tanA = sinA / cosA.

Also, 1 + tan²A = sec²A; sec²A - 1 = tan²A

\frac{\sqrt{secA-1} }{\sqrt{secA+1} } +\frac{\sqrt{secA+1} }{\sqrt{secA-1} } =\frac{(\sqrt{secA-1)}(\sqrt{secA-1})+(\sqrt{secA+1)}(\sqrt{secA+1}) }{(\sqrt{secA+1})(\sqrt{secA-1}) } \\\\=\frac{secA-1+(secA+1)}{\sqrt{sec^2A-secA+secA-1} } \\\\=\frac{2secA}{\sqrt{sec^2A-1} } \\\\=\frac{2secA}{\sqrt{tan^2A} } \\\\=\frac{2secA}{tanA} \\\\=\frac{2*\frac{1}{cosA} }{\frac{sinA}{cosA} }\\\\= 2*\frac{1}{cosA}*\frac{cosA}{sinA}\\\\=2*\frac{1}{sinAA}\\\\=2cosecA

You might be interested in
<img src="https://tex.z-dn.net/?f=6%20%5Cdiv%20131.4" id="TexFormula1" title="6 \div 131.4" alt="6 \div 131.4" align="absmiddle"
Svetradugi [14.3K]

Answer: 21.9

131.4 divided by 6

4 0
3 years ago
What is the greatest common factor of 128 and 96
aalyn [17]
The greatest common factor is 32

6 0
3 years ago
Read 2 more answers
What is the mean score Score<br> 90<br> 80<br> 70<br> 60
cupoosta [38]

Answer:

75

Step-by-step explanation:

Four scores....  add them together and divide by four

 (90 + 80 + 70 + 60) / 4 = 75

8 0
2 years ago
The decimal 0.3 represents 1/3. What type of number best describes 0.9, which is 3 times 0.3? Explain.
myrzilka [38]
It can be described as 9/10
8 0
3 years ago
Read 2 more answers
Total distance divided by total time is called what?
azamat
Speed is computed by dividing total distance by total time.

Speed = Total Distance / total time

From the above formula, we can derive the formula of time and distance.

Time = Distance / Speed

Distance = Speed x time



6 0
3 years ago
Other questions:
  • A _______ is a set of characters that uses the same typeface.
    14·1 answer
  • Write the polynomial in standard form 4g – g3 + 3g2 – 2
    9·2 answers
  • On a coordinate plane, triangle D E F has points (negative 8, 8), (10, negative 2), and (negative 8, negative 8). Find the area
    14·1 answer
  • The Millers put carpet on the floor of their living room. They bought 160 square feet of carpet. If the length of the room is 16
    7·1 answer
  • Lily grew 20 centimeters in 1 year. She is now 1.8 m tall. How tall was she 1 year ago?
    14·1 answer
  • (07.05 LC)
    6·2 answers
  • 1. Charlie bought a new computer for $450 with his credit card. He plans to pay the minimum payment
    8·1 answer
  • What is the next number in this geometric sequence?
    10·1 answer
  • Passes through (0, -4) and (-4,5)
    11·2 answers
  • MATH: EXPONENTIAL WORK PROBLEM 1. HELP PLEASE! 13 pts
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!